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Risk and Stochastics Seminar Series 2013-14

The Risk and Stochastics Seminar aims to promote communication and discussion of research in the mathematics of insurance and finance and their interface, to encourage interaction between practice and theory in these areas, and to support academically students in related programmes at postgraduate level. All are welcome to attend. Sessions run regularly during LSE terms. Please see below for individual times and locations of each talk.

The current up-to-date schedule is given below. Please contact Events| for further information about any of these seminars. All are very welcome to attend.  

24th October 2013

Budhi Arta Surya (SBM ITB) 12.00-13.00, COL 6.15. Columbia House

Title:  Optimal Capital Structure with Scale Effects under Spectrally Negative Levy Models

Abstract: The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of bankruptcy costs and tax benefits dependent on the firm's asset value. These effects have been empirically shown, among others, in Warner (1976), Ang et al. (1982), and Graham and Smith (1999). By using the fluctuation identities for the spectrally negative Levy process, we obtain a candidate bankruptcy level as well as a sufficient condition for optimality. The optimality holds in particular when, monotonically in the asset value, the value of tax benefits is increasing, the loss amount at bankruptcy is increasing, and its proportion relative to the asset value is decreasing. The solution admits a semi-explicit form, and this allows for instant computation of the optimal bankruptcy levels, equity/debt/firm values and optimal leverage ratios. A series of numerical studies are given to analyze the impacts of scale effects on the default strategy and the optimal capital structure.

Joint work with Kazutoshi Yamazaki

Links: http://arxiv.org/abs/1109.0897|

7th November 2013

Kostas Kardaras (LSE) 12.00-13.00, COL 6.15. Columbia House

Title:  Equilibrium in risk-sharing games

Abstract: A market is considered with several acting financial agents, whose aim is to increase their utility by efficiently sharing their random endowments. Given the endogenously derived optimal sharing rules, we consider the situation where agents do not reveal their true endowments, but instead report as endowments the random quantities that maximise their utility when the sharing rules are applied. Under exponential utilities (coinciding with entropic risk measures), an analysis of Nash equilibrium is carried out, where it is shown in particular that the optimal contract of each agent possesses endogenous bounds only depending on the agents' risk tolerance, and not on their random endowment. Existence and uniqueness of Nash equilibrium for the 2-player game is obtained. Furthermore, it is discussed how such an equilibrium benefits extremely high risk tolerance agents and results in risk-sharing inefficiency.

Joint work with M. Antropelos.

11th November 2013

Claudio Fontana (INRIA Paris) 12.00-13.00, CLM 6.02. Clement House

Title:  On honest times and arbitrage possibilities.

Abstract:   In the context of a general continuous financial market model, we study whether the additional information associated with an honest time T gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that arbitrage profits can never be realised strictly before T, while classical arbitrage opportunities can be realised exactly at T as well as after T. Moreover, arbitrages of the first kind can only be obtained by starting to trade as soon as T occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than no free lunch with vanishing risk. Finally, we discuss extensions of the theory to the case of general semi martingale models.

18th November 2013

Martin Larsson (EPFL) 12.00-13.00, CLM 6.02. Clement House

Title:  Polynomial preserving diffusions and models of the term structure

Abstract:  Polynomial preserving processes are multivariate Markov processes that extend the important class of affine processes. They are defined by the property that the semigroup leaves the space of polynomials of degree at most $n$ invariant, for each $n$, which lends significant tractability to models based on these processes. In this talk I will discuss existence and uniqueness of polynomial preserving diffusions, a task which is made nontrivial due to degenerate and non-Lipschitz diffusion coefficients, as well as a complicated geometric structure of the state space. I will then discuss how polynomial preserving processes can be used to build term structure models that accommodate three features that are otherwise difficult to combine: nonnegative short rates, tractable swaption pricing, and unspanned factors affecting volatility and risk premia.

25th November 2013

Giorgia Callegaro (University of Padova)
12.00-13.00, CLM 6.02. Clement House

Title:  An application to credit risk of a hybrid Monte Carlo–optimal quantization method.

Abstract:   In this paper we use a hybrid Monte Carlo-Optimal quantization method to approximate the conditional survival probabilities of a firm, given a structural model for its credit default, under partial information.

We consider the case when the firm's value is a non-observable stochastic process ${(V_t)}_{t \ge 0}$ and investors in the market have access to a process ${(S_t)}_{t \ge 0}$, whose value at each time $t$ is related to $(V_s, 0 \le s \le t)$.

We are interested in the computation of the conditional survival probabilities of the firm given the ``investor's information''.

As an application, we analyze the shape of the credit spread curve for zero coupon bonds in two examples. Calibration to available market data is also analysed.

2nd December 2013

Johannes Muhle-Karbe (ETH Zurich) 
12.00-13.00, CLM 6.02. Clement House

Title:  Optimal Liquidity Provision in Limit Order Markets

Abstract:  A small investor provides liquidity at the best bid and ask prices of a limit order market. For small spreads and frequent orders of other market participants, we explicitly determine the investor's optimal policy and welfare. In doing so, we allow for general dynamics of the mid price, the spread, and the order flow, as well as arbitrary preferences of the liquidity provider under consideration.

Joint work with Christoph Kühn.

9th December 2013 

Igor Evstigneev (Manchester) 12.00-13.00, CLM 6.02, Clement House

Title: Modelling Dynamics and Equilibrium of Asset Markets: A Behavioral Approach

Abstract: Conventional models of dynamic equilibrium in asset markets are based on the principles of General Equilibrium theory (Walras, Arrow, Debreu, Radner and others). This theory in its classical form assumes that market participants are fully rational and their goals can be described in terms of the maximization of utilities subject to budget constraints. The objective of this work is to develop an alternative modelling approach admitting that market participants may have a whole variety of other patterns of behavior determined by their individual psychology, not necessarily reducible to fully rational utility maximization. The models developed do not rely upon restrictive hypotheses (perfect foresight) and avoid using unobservable agents’ characteristics such as individual utilities and beliefs, which makes them amenable to quantitative practical applications. The results obtained are concerned with fundamental questions and problems in Financial Economics such as equilibrium asset pricing and portfolio selection. The modelling frameworks combine stochastic dynamic games and evolutionary game theory. The methods employed are based on the stochastic stability analysis of nonlinear random dynamical systems.

Joint work with
Rabah Amir, Economics Department, University of Iowa
Thorsten Hens, Department of Banking and Finance, University of Zurich
Klaus R. Schenk-Hoppé, School of Mathematics and Business School, University of Leeds

13th January 2014

Agostino Capponi (Purdue University)
12.00-13.00, CLM 6.02, Clement House

Title: Optimal Investment in Defaultable Securities under Information Driven Default Contagion

Abstract: We introduce a novel portfolio optimization framework where a power investor decides on optimal portfolio allocations within an information driven default contagion model. The investor can allocate his wealth across several defaultable stocks whose growth rates and default intensities are driven by a hidden Markov chain. The latter acts as a frailty factor introducing dependency across defaults and affecting future comovements of security prices.
By a suitable measure change, we reduce the partially observed stochastic control problem to an equivalent fully observed risk-sensitive control problem, where the state is given by the regime filtered probabilities. Using the dynamic programming principle, we then provide an analysis of default contagion manifested through dependence of the optimal strategies on the gradient of value functions in one-to-one correspondence with the default states of the economy. We prove a verification theorem showing that each value function is recovered as the generalized solution of the corresponding HJB PDE. We deal with the quadratic growth of the gradient and exponential nonlinearity coming from default contagion by considering a variational representation of our problem, establishing uniform bounds for solutions to a sequence of approximation problems, and showing their convergence to the unique generalized solution of the corresponding HJB PDE in a suitably chosen Sobolev space.

20th January 2014

Hansjoerg Albrecher (HEC Lausanne)
12.00-13.00, CLM 6.02, Clement House

Title:  On theoretical and practical aspects of catastrophe insurance

Abstract:  In this talk we give an overview of some recent results and developments in the modelling of insurance risk related to natural catastrophes. In addition to some theoretical results on the statistics of such extremal events, we present a study of flood and storm risk in Austria. The feasibility of the general principle of time diversification in this context is also discussed.

27th January 2014

René Aid (EDF)
12.00-13.00, CLM 6.02, Clement House

Title:  A high-dimensional investment model in electricity generation

Abstract:  In this talk, we will show how the progresses made in the
recent decade in numerical methods for optimal stopping time problems
and optimal switching problems allow to design efficient and yet
realistic models to study the dynamic of investment in electricity
generation. We will give the example of a high-dimensional electricity
generation investment model. This model takes into account electricity
demand, cointegrated fuel prices, carbon price and random outages of
power plants. The evolution of the optimal generation mix is
illustrated on a realistic numerical problem in dimension 8, i.e. with
2 different technologies and 6 random processes.
This talk is based on a joint work with Luciano Campi, Nicolas Langrene and Huyen Pham.

3rd February 2014

Claude Martini (Zeliade Systems)
12.00-13.00, CLM 6.02, Clement House

Title:  Calibration of the SSVI model and applications to model free option pricing bounds’

Abstract:  Gatheral and Jacquier achieved in 2012 a consistent (arbitrage-free) extension of the parametric SVI model in the maturity dimension. This Surface SVI (SSVI) model is parameterized by a correlation coefficient and a function which corresponds to the curvature of the smile at each maturity. We go through a re-parameterization of the SSVI model that lends itself to a nice 2-stages calibration procedure. Calibration examples on CBOE SPX delayed quotes are provided. Since the SSVI model does calibrate very well, we eventually get an explicit arbitrage-free parameterization of the market implied volatility surface. We compute the model-free Beiglböck-Juillet-Touzi-Henry Labordère optimal transport bounds of an exotic option in this setting. An executable version of this work is available on the Zanadu platform (joint work with I.Laachir, ENSTA and Zeliade Systems). (Keywords: implied volatility, SVI, calibration, Optimal Transport option bounds)

5th February 2014

Walter Schachermayer (University of Vienna)
16.00-17.00, CLM 3.07, Clement House

Title:  Duality Theory for Portfolio Optimisation under Transaction Costs

Abstract: In this talk, we develop a dynamic duality theory for portfolio optimisation under proportional transaction costs with cadlag price processes. In particular, we provide examples that illustrate the new effects arising from the combination of the transaction costs and jumps of the underlying price process. 

The talk is based on joint work with Christoph Czichowsky.

10th February 2014

Anna Aksamit (Université d'Evry Val d'Essonne)
12.00-13.00, CLM 6.02, Clement House

Title: Optional semimartingale decomposition and non-arbitrage condition in enlarged filtration

Abstract:  Our study addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon or when a random variable satisfying Jacod's hypothesis is incorporated. Precisely, we focus on the No-Unbounded-Profit-with-Bounded-Risk condition, which is also known in the literature as the first kind of non-arbitrage. In the general semimartingale setting, we provide a necessary and sufficient condition on the random time for which the non-arbitrage is preserved for any process. Analogous result is formulated for initial enlargement with random variable satisfying Jacod's hypothesis. Moreover we give an answer to a stability of non-arbitrage question for fixed process. The crucial intermediate results in enlargement of filtration theory are obtained. For local martingales from the reference filtration we provide special optional semimartingale decomposition up to random time and in initially enlarged filtration under Jacod's hypothesis. An interesting link to absolutlety continuous change of measure problem is observed. 

This is a joint work with Tahir Choulli, Jun Deng and Monique Jeanblanc.

17th February 2014

Antoine Jacquier (Imperial College)
12.00-13.00, CLM 6.02, Clement House

Title: Asymptotics of forward implied volatility

Abstract: We study the asymptotic behaviour of the forward implied volatility (namely the implied volatility corresponding to forward-start European options). Our tools rely on (finite-dimensional) large deviations and saddlepoint analysis, albeit not necessarily relying on standard convexity arguments. We shall also relate this to the Freidlin-Wentzell approach for sample paths. From a practical point of view, this sheds light on the dynamics of forward implied volatilities, which we highlight numerically in the Heston model. 

3rd March 2014

Yu-Jui Huang (Dublin City University)
12.00-13.00, CLM 6.02, Clement House

Title:  Model-independent Superhedging under Portfolio Constraints

Abstract:  In a discrete-time market, we study the problem of model-independent superhedging of exotic options under portfolio constraints. The superhedging portfolio consists of static positions in liquidly traded vanilla options, and a dynamic trading strategy, subject to certain constraints, on the risky asset. By the theory of Monge-Kantorovich optimal transport, we establish a superhedging duality, which admits a natural connection to convex risk measures. With the aid of this duality, we derive a model-independent version of the fundamental theorem of asset pricing under portfolio constraints. It is worth noting that our method covers a large class of Delta constraints as well as Gamma constraint.

10th March 2014

Giorgio Ferrari (Bielefeld University)
12.00-13.00, CLM 6.02, Clement House

Title:  A Stochastic Partially Reversible Investment Problem on a Finite Time-Horizon: Free-Boundary Analysis

Abstract: We study a continuous-time, finite horizon, stochastic partially reversible investment problem for a firm producing a single good in a market with frictions. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investment-disinvestment problem a zero-sum optimal stopping game and characterize its value function through a free-boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diffusion reflected at the two boundaries. 

17th March 2014

Sergio Pulido (EPFL)
12.00-13.00, CLM 6.02, Clement House

Title:  Markovian cubature rules for polynomial preserving processes

Abstract: Polynomial preserving processes are defined as time-homogeneous Markov jump-diffusions whose generator leaves the space of polynomials of any fixed degree invariant. Polynomial preserving processes include affine processes, whose transition functions admit an exponential-affine characteristic function. These processes are attractive for financial modeling because of their tractability and robustness. In this work we study Markovian cubature rules for polynomial preserving processes. These rules aim to exploit the defining property of polynomial preserving processes in order to reduce the complexity of the implementation of such models. More precisely, we study conditions guaranteeing the existence of finite-state Markov processes that match the moments of a given polynomial preserving process. The states of these processes together with their transition probabilities can be interpreted as Markovian cubature rules. We first give a characterization theorem for the existence of Markovian cubature rules in continuous time. This theorem illustrates the complexity of the problem by combining algebraic and geometric considerations. We show that for polynomial preserving diffusions, there are no continuous-time Markovian cubature rules for high order moments. We provide a positive result by showing that the construction is possible when one considers finite-state Markov chains on lifted versions of the state space. Additionally, by relaxing the continuous-time cubature problem, we can construct discrete time finite-state Markov processes that match moments of arbitrary order. This discrete time construction relies on the existence of long-run moments for the polynomial process and cubature rules over these moments.
This is joint work with Damir Filipovic and Martin Larsson.


Michael Schroeder| (VU Amsterdam)
12.00-13.00, STC S.75, St Clements

Title: Volatility smiles and derivatives - a direct route to new kinds of high-dimensionality?

Abstract: FX-rates provide the textbook example for financial instruments that are not just traded in a 24/7 fashion but quoted in real time over the entire year. FX-derivatives are similar in their liquidity, but completely different in character. FX-options, for example, are famously liquidly traded at most 5 strikes and 10 maturities; their design is subordinated to the daily 4pm-GMT-fixings. We will outline methods to handle such institutional discetenesses in model-based  approaches to derivatives. Highlighting recent stochastic volatility models of Ornstein-Uhlenbeck type, this will include methods for model calibration based on discretely-sampled generalized BS-formulas. We will also report on exact valuation methods for discretely-sampled Asian options (as part of an LSE-project with M. Frentz (Bank of Sweden)).


Elena Boguslavskaya| (Brunel University)
13.00-14.00, Room 32L G.08, 32 Lincoln's Inn Fields

Title: An effective method to solve optimal stopping problems for Lévy processes in infinite horizon or how to avoid differential or integro-differential equations while solving an optimal stopping problem for a Lévy problem

Abstract: We present a method to solve optimal stopping problems in infinite horizon for a Levy process when the reward function $g$ can be non-monotone.

To solve the problem we introduce two new objects. Firstly, we  define a random variable $\eta(x)$ which corresponds to the $\argmax$ of the reward function. Secondly, we propose a certain integral transform which can be built on any suitable random variable.  It turns out that this integral transform constructed from $\eta(x)$ and applied to the reward function produces an easy and straightforward description of the optimal stopping rule. We illustrate our results with several examples.

The method we propose allows to avoid complicated differential or integro-differential equations which arise if the standard methodology is used.

The talk is based on the following paper:


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