2017
Tuesday 14 March - Junwei Xu (LSE) presents his own work
Tuesday 7 March - Denis Schelling (LSE) presents his own work
Tuesday 21 February - Weiguan Wang (LSE) presents his own work
Tuesday 7 February - Yang Guo (LSE) presents his own work
Tuesday 31 January - Michael Kusnetsov (LSE) presents his own work
Tuesday 24 January - Thomas Bernhardt (LSE) presents his own work
Tuesday 17 January - Jose Pasos (LSE) presents his own work
2016
Tuesday 6 December - Jose Pasos (LSE) and Thomas Bernhardt (LSE)
Tuesday 15 November - Michael Kusnetsov (LSE) and Junwei Xu (LSE)
Tuesday 8 November - Yang Guo (LSE)
Tuesday 1 November - Denis Schelling (LSE)
Tuesday 29 October - Michael Kusnetsov (LSE)
Tuesday 18 October - Weiguan Wang (LSE)
Thursday 24 March
Denis Schelling (LSE) - Mean-variance hedging
Michael Kusnetsov (LSE) - Clearing solutions in interbank networks with two maturities
Tuesday 15 March - Abdulla Al-Othman (LSE)
Equilibria in financial markets
Tuesday 8 March - Junwei Xu (LSE)
Optimal liquidation in an Almgren-Chriss type model with Lévy processes and finite time horizons
We consider an Almgren-Chriss type liquidation model and aim to maximise the expected exponential utility of the cash position at a given finite time. The unaffected asset price follows a Levy process which may provide a good statistical fit to observed asset price data for short time horizons. The temporary price impact is described by a general function, satisfying some reasonable conditions. We reduce the problem to a deterministic optimisation problem and we derive the optimal liquidation strategy and the corresponding value function in closed forms. It turns out that, if the unaffected asset price has a positive drift, then it might be optimal to wait for a while during selling, or it might be optimal to buy back at the beginning of trading, and price manipulation is allowed in the case of positive drift. We solve the deterministic optimisation problem using calculus of variations. To this end, the Beltrami identity approach doesn't apply in a classical sense because the integrand in the objective functional is not sufficiently smooth. Nonetheless, we establish necessary and sufficient conditions for the optimiser in a fairly general setting. In particular, we characterise the optimiser using the Beltrami identity, which is a first order ordinary differential equation. This characterisation allows us to get a closed-form solution.
Tuesday 1 March - Thomas Bernhardt (LSE)
Ito-Semi-Diffusions, a Tool to approximate Levy Processes
We are interested in processes which are distributed like Levy processes at certain time points and can be described as homogeneous diffusions between these points. We are going to analyse when such processes converge in distribution if the mesh size of the time points is going to zero. Furthermore, we are considering the existence of martingale measures for a fixed time-grid (linking the pricing problem for Levy processes approximately to the one for the above processes).
Tuesday 16 February - Jose Pasos (LSE)
Irreversible capacity expansion with possible default
We consider the problem of determining the optimal capacity expansion strategy that a firm operating within a random economic environment should adopt. We model market uncertainty by means of a general one-dimensional positive diffusion with possible absorption at 0. The objective is to maximise a performance criterion that involves a general running payoff function and associates a cost with each capacity increase up to the first hitting time of 0, at which time the firm defaults. The resulting optimisation problem takes the form of a degenerate two-dimensional singular stochastic control problem that we explicitly solve. We further illustrate our general results in the special cases where market uncertainty is modelled by a Brownian motion with drift, a geometric Brownian motion or a square-root process such as the one in the CIR model.
2015
Tuesday 8 December
Discussion led by Abdulla Al-Othman: equilibria in financial markets
Tuesday 1 December
Discussion led by Jose Pasos: equilibria in financial markets
Tuesday 24 November
Discussion led by Thomas Bernhardt: equilibria in financial markets
Tuesday 17 November
Discussion led by Junwei Xu (LSE): equilibria in financial markets
Tuesday 10 November
Discussion led by Denis Schelling (LSE): equilibria in financial markets
Tuesday 3 November
Discussion led by Michael Kusnetsov (LSE): equilibria in financial markets
Tuesday 20 October
Discussion of Michaelmas Term 2015 topic: equilibria in financial markets
Tuesday 13 October - Denis Schelling (LSE)
Portfolio Optimisation
I will be presenting my master thesis supervised by Johannes Muhle-Karbe, where I worked with a continuous-time self-financing condition taking into account features of high-frequency markets developed in Carmona and Webster (2013). The first part of the talk will be dedicated to the derivation of this equation and the empirical phenomena it relies on. I will then introduce the problem of mean-variance portfolio selection in a simple buy-and-hold setup and discuss utility maximisation when using this model. I will conclude my presentation by giving the main results obtained in this thesis.
Tuesday 17 March - Yavor Stoev (LSE)
Presented his current work
Tuesday 10 March - Jose Pasos (LSE)
A model for Long-term Irreversible Capital Investment
We consider a model for a company’s project where an economic indicator (such as a price) measures how favourable market conditions are for the company’s products. Depending on the state of the indicator, the investor can increase the project’s capital until default or bankruptcy time is reached, however decreasing capital is not allowed. The problem consists of determining the strategies which optimal profit once the cost of investment is discounted. Mathematically, this model is a singular stochastic control problem which, under suitable assumptions, admits explicit solutions.
Tuesday 3 March - Michael Kusnetsov (LSE)
Presented his current work
Tuesday 24 February - Junwei Xu (LSE)
Optimal liquidation in the Almgren-Chriss framework with Levy processes
We consider an optimal liquidation problem in the Almgren-Chriss framework with infinite time horizon. The unaffected asset price is driven by a Levy process. The temporary price impact is described by a general function. We maximise the utility of an investor with constant absolute risk aversion, showing that the problem can be reduced to be over a set of deterministic admissible strategies. The optimal liquidation strategy is solved out explicitly by an optimal control approach. Moreover, we derive a Levy process which is a linear approximation to an exponential Levy process. Then starting from exponential Levy price, by using linear approximation, we show that the widely used power-law temporary impact function gives out an impractical strategy such that it is optimal to sell almost all shares in an extremely short time period. Hence, a new type of impact function, as a combination of power and exponential laws, is suggested.
Tuesday 17 February - Thomas Bernhardt (LSE)
An Existence Theorem for Weak Solutions of Homogeneous SDEs with time-dependent Boundaries
No abstract available
Tuesday 10 February - Dr Yerkin Kitapbayev (University of Manchester)
Swing options
Swing options are particular financial derivatives that may be described as American options with multiple exercises. They are widely traded in the energy markets and usually the option's underlying asset is the price of a given commodity. In mathematical terms the price of an option of this kind is described by the value function of an optimal stopping problem with multiple stopping times.
We assume that the dynamics of the price is a geometric Brownian motion and study the Swing put option on finite time horizon and two exercise rights. An important parameter of this problem is the so-called refraction period. It can be interpreted as the minimal period that the option's seller needs to deliver a new portion of asset. The double optimal stopping problem reduces to standard single optimal stopping problem. Analysis of optimal exercise region gives a remarkable result: unlike the American put option problem with single optimal exercise boundary our problem has two boundaries, one is below the strike price, other one is above.
Using the local time-space calculus we derive a closed form expression for the option's price in terms of the optimal exercise boundaries for both exercise rights and show that the couple of optimal exercise boundaries for the first exercise can be characterised as the unique solution to system of nonlinear integral equations. This system is then evaluated numerically.
Tuesday 3 February - Mathieu Dubois (LSE)
Switching Stochastic Volatility Models and Option Pricing
Tuesday 27 January - Christoph Czichowsky (LSE)
Presented his current work
Tuesday 20 January - Abdulla Al-Othman (LSE)
Presented his current work