Home > Department of Statistics > Events > 2014-15 Seminar Series > Joint Risk and Stochastics and Financial Mathematics Seminar Series 2014-15

Department of Statistics

Columbia House

London School of Economics

Houghton Street

London

WC2A 2AE

General enquiries about events and seminars in the Department of Statistics

BSc Queries

+44 (0)20 7955 7650

MSc Queries

+44 (0)20 7955 6879

MPhil/PhD Queries

+44 (0)20 7955 7511
Email: i.marshall@lse.ac.uk

# Joint Risk and Stochastics and Financial Mathematics Seminar Series 2014-15

The Joint Risk and Stochastics and Financial Mathematics Seminar Series 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.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 16 October 2014: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Scott Robertson
Carnegie Mellon University

Title: Indifference pricing for contingent claims: large deviations effects

Abstract: In this talk, we consider utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors, making connections with the theory of large deviations. This work is motivated by the recent explosive growth in the derivatives market; in particular we seek to explain why such positions are being taken and what the effects are in terms of pricing. To make the analysis tractable, we concentrate on sequences of semi-complete markets where for each n the claim h_n admits the decomposition h_n = D_n+Y_n where D_n is replicable and Y_n is completely unhedgeable in that the indifference price of Y_n for an exponential investor is its certainty equivalent. Under broad conditions, we may assume that Y_n vanishes in accordance with a large deviations principle as n grows. In this setting, we identify limiting indifference prices as the position size becomes large, and show the prices typically are not the unique arbitrage free price in the limiting market. Furthermore, we show that optimal purchase quantities occur at the large deviations scaling, and hence large positions endogenously arise in this setting.

Joint work with Konstantinos Spiliopoulos.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 30 October 2014: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Samuel Drapeau
Humboldt Universität zu Berlin

Title: Numerical representation of convex preferences on Anscombe–Aumann acts

Abstract: We study the preferences of agents for diversification and better outcomes when they are facing both, in Frank Knight's formulation, measurable as well as unmeasurable uncertainty. Following Anscombe and Aumann, such a situation can be modeled by preferences expressed on stochastic kernels, that is scenario dependent lotteries. By means of automatic continuity methods based on Banach-Dieudonné's Theorem on Fréchet spaces, we provide a robust representation. This gives us some insight into the nature of uncertainty aversion these preferences are expressing. We further investigate under which conditions these two intricate dimensions of uncertainty can be disentangle into a distributional uncertainty, in the direction of von Neumann and Morgenstern's theory, and a probability model uncertainty, in the spirit of risk measures. These results allow in particular to address both Allais as well as Elsberg's paradox.

Joint work with Patrick Cheridito, Freddy Delbaen and Michael Kupper.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 13 November 2014: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Title: Marking-to-market and price impact

Abstract: The paper studies incentives and trading decisions of money managers who trade in markets with price impact. I show that in markets with price impact the practice of marking-to-market funds' assets creates incentives for managers to accumulate excessively large positions. This trading behaviour may force prices away from their fundamental levels for a long time and may result in large losses for investors.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 20 November 2014: 12pm - 1pm, Room NAB 1.09, New Academic Building
THIS TIME AND VENUE IS CANCELLED

Please note that this talk will now take place as part of the London Mathematical Finance Seminar series at King's College London, Strand campus, on Thursday 20 November 2014, starting at 17:45

Title: Existence and uniqueness results for multi-dimensional quadratic BSDEs arising from a price impact model with exponential utility

Abstract: In this work we study multi-dimensional systems of quadratic BSDEs arising from a price impact model where an influential investor trades illiquid assets with a representative market maker with exponential preferences. The impact of the strategy of the investor on the prices of the illiquid assets is derived endogenously through an equilibrium mechanism. We show that a relationship exists between this equilibrium mechanism and a multi-dimensional system of quadratic BSDEs. We also specify conditions on the parameters of the model that guarantee that the system of BSDEs has a unique solution, which corresponds to a family of unique equilibrium prices for the illiquid assets. The proof relies on estimates that exploit the structure of the equilibrium problem. Finally, we provide examples of parameters for which the corresponding system of BSDEs in not well-posed.

Joint work with Dmitry Kramkov.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 27 November 2014: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Jan-Henrik Steg
Universität Bielefeld

Title: Symmetric equilibria in stochastic timing games

Abstract: We construct subgame-perfect equilibria with mixed strategies for symmetric stochastic timing games with arbitrary strategic incentives. The strategies are qualitatively different for local first- or second-mover advantages, which we analyse in turn. When there is a local second-mover advantage, the players may conduct a war of attrition with stopping rates that we characterize in terms of the Snell envelope from the general theory of optimal stopping, which is very general but provides a clear interpretation. With a local first-mover advantage, stopping typically results from pre-emption and is abrupt. Equilibria may differ in the degree of pre-emption, precisely at which points it is triggered. We provide an algorithm to characterize where pre-emption is inevitable and to establish the existence of corresponding payoff-maximal symmetric equilibria.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 22 January 2015: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Georgy Chabakauri
LSE (Department of Finance)

Title: Multi-asset noisy rational expectations equilibrium with contingent claims

Abstract: We consider a noisy rational expectations equilibrium in a multi-asset economy populated by informed and uninformed investors, and noise traders. Informed investors privately observe an aggregate risk factor affecting the probabilities of different states of the economy. Uninformed investors attempt to extract that information from asset prices, but full revelation is prevented by noise traders. We relax the usual assumption of normally distributed asset payoffs and allow for assets with more general payoff distributions, including contingent claims, such as options and other derivatives. We show that assets reveal information about the risk factor only if they help span the exposure of probabilities of states to the risk factor. When the market is complete, we provide equilibrium asset prices and optimal portfolios of investors in closed form. In incomplete markets, we derive prices and portfolios in terms of easily computable inverse functions.

Joint work with Kathy Yuan and Konstantinos E Zachariadis.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 5 February 2015: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Michael Schmutz
University of Bern and Swiss Financial Market Supervisory Authority (FINMA)

Title: Challenges in risk based solvency frameworks

Abstract: Risk-based solvency frameworks such as Solvency II to be introduced in the EU or the Swiss Solvency Test (SST) in force since 2011 in Switzerland seek to assess the financial health of insurance companies by quantifying the capital adequacy through calculating the solvency capital requirement (SCR). Companies can use their own economic capital models (internal models) for this calculation, provided the internal model is approved by the insurance supervisor. The Swiss supervisor has essentially completed the first round of internal model approvals. This has provided the supervisor and the industry with many insights into the challenges of designing, assessing, and supervising such models and has shown that there is a considerable number of challenges, in particular modelling challenges, that have not yet been solved in a completely satisfactory way. Some of the most important challenges and problems will be discussed along with some approaches to solutions.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 19 February 2015: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Pietro Siorpaes
University of Oxford

Title: Optimal investment and price dependence in a semi-statistic market

Abstract: We study the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously in time. Using a general utility function defined on the positive real line, we first study existence and uniqueness of the solution, and then we consider the dependence of the outputs of the utility maximization problem on the price of the derivatives, investigating not only stability but also differentiability, monotonicity, convexity and limiting properties.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 26 February 2015: 12pm - 1pm, NAB 1.09, New Academic Building
Maps and directions

Anastasia Ellanskaya
LAREMA - Université Angers

Title: Utility maximisation and utility indifference price for exponential semi-martingale models and HARA utilities

Abstract: We consider the utility maximisation problem for semi-martingale models and HARA (hyperbolic absolute risk aversion) utilities. Using specific properties of HARA utilities, we reduce the initial maximisation problem to the conditional one, which we solve by applying a dual approach. Then we express the solution of the conditional maximisation problem via conditional information quantities related to HARA utilities, like the Kullback–Leibler information and Hellinger-type integrals. In turn, we express the information quantities in terms of information processes, which is helpful in indifference price calculus. Finally, we give equations for indifference prices. We apply the results to Black–Scholes model with correlated Brownian motions, jump-diffusion model and Lévy model and give an explicit expression for information quantities. Then the previous formulas for the indifference price can be applied.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 5 March 2015: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Fausto Gozzi
Luiss University

Title: Impact of time illiquidity in a mixed market without full observation

Abstract: In this talk we present and study a class of optimal portfolio problems in a two-assets market where one asset is illiquid in the sense that it can be traded only at given random times (of exponential law) and it cannot be fully observed. This feature arises in many cases in real markets and it clearly modifies the optimal policies with respect to the benchmark given by the standard Merton model. We first recall the Merton model, then introduce a model of Pham and Tankov, where only one illiquid asset is present: we show how to solve this model by the dynamic programming approach. Then we consider the more difficult case of two correlated assets with partial observation and show how the dynamic programming approach also applies to this case in a satisfactory way. We also give some numerical experiment to evaluate the impact of the illiquidity and of the lack of full observation.

Joint paper(s) with Salvatore Federico and Paul Gassiat.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 19 March 2015: 12pm - 1pm, Room NAB 1.09, New Academic Building
Maps and directions

Dylan Possamaï
CMAP École polytechnique

Title: A primer on Principal/Agent models and their recent extensions

Abstract: We will present the main ideas and intuitions behind the modelization of the so-called principal/agent models, which are at the heart of the contracting theory. The theory emerged in the 70s from the acknowledgment that almost everything in economics was to a certain degree a matter of incentives (incentives to work hard, to produce, to study, to invest, to consume reasonably…) and the fact that such situations could not be reproduced using the general equilibrium theory. While a great number of studies were devoted to quite comprehensive models in discrete time, their continuous-time counterparts have only recently received a lot attention from the economics literature, starting with the breakthrough works of Holmstrom and Milgrom or later on of Sannikov. We will review the modelization of these problems, both in the cases of moral-hazard and adverse selection and see the type of mathematical tools that can be used to treat them. Moreover, if time permits, we will try to look at some recent generalizations of the theory, as well as still open problems.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desks to facilitate your access into the New Academic Building.

Thursday 28 May 2015: 12pm - 1pm, Room OLD 3.28, Old Building (Houghton Street)
Maps and directions

Martin Herdegen
ETH Zürich

Title: Sensitivity of optimal consumption streams

Abstract: We study the sensitivity of optimal consumption streams with respect to perturbations of the random endowment. We show that to the leading order, any consumption correction for the perturbed endowment is still optimal as long as the budget constraint is binding. More importantly, we also establish the optimal correction at the next-to leading order. This can be computed in two steps. First, one has to find the optimal correction for a deterministic perturbation. This only involves the risk-tolerance process of the unperturbed problem and yields a risk-tolerance martingale and a corresponding risk-tolerance measure. If the risk-tolerance process and the interest rate are deterministic, the latter is constant. In a second step, one can then calculate the optimal correction for any random perturbation. This is given by an explicit formula whose key ingredients are the conditional expectations of the terminal cumulative perturbation and the integrated risk-tolerance process under the risk-tolerance measure.

Joint work with Johannes Muhle-Karbe.

If you are not an LSE member of staff or LSE student please email Ian Marshall with details of the seminar(s) you would like to attend so that we can notify the security reception desk to facilitate your access into the appropriate building(s)

Share:|||