Past Mathematical Finance Internal Seminar

22 January 2009
13:00
Vicky Henderson
Abstract
We solve the problem of an agent with prospect theory preferences who seeks to liquidate a portfolio of (divisible) claims. Our methodology enables us to consider different formulations of prospect preferences in the literature (piecewise exponential or piecewise power) and various price processes. We find that these differences in specification matter - for instance, with piecewise power functions, the agent may liquidate at a loss relative to break-even, albeit the likelihood of liquidating at a gain is much higher than liquidating at a loss. This is consistent with the disposition effect documented in empirical and experimental studies. We find the agent does not choose to partially liquidate a position, but rather, if liquidation occurs, the entire position is sold. This is in contrast to partial liquidation when agents have standard concave utilities.
  • Mathematical Finance Internal Seminar
27 November 2008
13:00
Jan Obloj
Abstract
I consider the problem of maximising the final utility of a portfolio which is constrained to satisfy the draw-down condition, i.e. the current value of the portfolio can not drop below a pre-specified funciton of its running maximum. It turns out that martingale techniques yield an explicit and rather elegant solution. The so- called Azema-Yor processes appear naturally and I take some time to introduce this class and discuss some of their remarkable properties. In particular, I show how they can be characterised as (unique, strong) solutions to SDEs called the Bachelier Eq and the Draw-Down Eq. The talk is based (in particular) on a joint work with L. Carraro, N. El Karoui and A. Meziou.
  • Mathematical Finance Internal Seminar
13 November 2008
13:00
Sam Howison
Abstract
I shall discuss a number of problems to do with approximating the value function of an American Put option in the Black-Scholes model. This is essentially a variant of the oxygen-consumption problem, a parabolic free boundary (obstacle) problem which is closely related to the Stefan problem. Having reviewed the short-time behaviour from the perspective of ray theory, I shall focus on constructing approximations in the case when there is a discretely paid dividend yield.
  • Mathematical Finance Internal Seminar
30 October 2008
13:00
Xunyu Zhou
Abstract
A new portfolio choice model in continuous time is formulated and solved, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as the decision variable. This formulation covers and leads to solutions to many existing and new models including expected utility maximisation, mean-variance, goal reaching, VaR and CVaR, Yaari's dual model, Lopes' SP/A model, and behavioural model under prospect theory.
  • Mathematical Finance Internal Seminar
16 October 2008
13:00
John Quah
Abstract
We identify a natural way of ordering functions, which we call the interval dominance order, and show that this concept is useful in the theory of monotone comparative statics and also in statistical decision theory. This ordering on functions is weaker than the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our monotone comparative statics results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the comparative statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics - specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann's (1988) concept of informativeness – generalize to payoff functions that obey the interval dominance order.
  • Mathematical Finance Internal Seminar
5 June 2008
13:00
Albina Danilova
Abstract
We study an equilibrium model for a defaultable bond in the asymmetric dynamic information setting. The market consists of noise traders, an insider and a risk neutral market maker. Under the assumption that the insider observes the firm value continuously in time we study the optimal strategies for the insider and the optimal pricing rules for the market maker. We show that there exists an equilibrium where the insider’s trades are inconspicuous. In this equilibrium the insider drives the total demand to a certain level at the default time. The solution follows from answering the following purely mathematical question which is of interest in its own: Suppose Z and B are two independent Brownian motions with B(0)=0 and Z(0) is a positive random variable. Let T be the first time that Z hits 0. Does there exists a semimartingale X such that 1) it is a solution to the SDE dX(t) = dB(t) + g(t,X(t),Z(t))dt with X(0) = 1, for some appropriate function g, 2) T is the first hitting time of 0 for X, and 3) X is a Brownian motion in its own filtration?
  • Mathematical Finance Internal Seminar
22 May 2008
13:00
Michael Monoyios
Abstract
We consider the hedging of a claim on a non-traded asset using a correlated traded asset, when the agent does not know the true values of the asset drifts, a partial information scenario. The drifts are taken to be random variables with a Gaussian prior distribution. This is updated via a linear filter. The result is a full information model with random drifts. The utility infdifference price and hedge is characterised via the dual problem, for an exponential utility function. An approximation for the price and hedge is derived, valid for small positions in the claim. The effectiveness of this hedging strategy is examined via simulation experiments, and is shown to yield improved results over the Black-Scholes strategy which assumes perfect correlation.
  • Mathematical Finance Internal Seminar
8 May 2008
13:00
Hanqing Jin
Abstract
In a financial market, the appreciate rates are very difficult to estimate precisely, and in general only some confidence interval will be estimated. This paper is devoted to the portfolio selection with the appreciation rates being in a certain closed convex set rather than some precise point. We study the problem in both expected utility framework and mean-variance framework, and robust solutions are given explicitly in both frameworks.
  • Mathematical Finance Internal Seminar
24 April 2008
13:00
Christopher Reisinger
Abstract
(based on joint work with Helen Haworth, William Shaw, and Ben Hambly) The simulation of multi-name credit derivatives raises significant challenges, among others from the perspective of dependence modelling, calibration, and computational complexity. Structural models are based on the evolution of firm values, often modelled by market and idiosyncratic factors, to create a rich correlation structure. In addition to this, we will allow for contagious effects, to account for the important scenarios where the default of a number of companies has a time-decaying impact on the credit quality of others. If any further evidence for the importance of this was needed, the recent developments in the credit markets have furnished it. We will give illustrations for small n-th-to-default baskets, and propose extensions to large basket credit derivatives by exploring the limit for an increasing number of firms
  • Mathematical Finance Internal Seminar

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