The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Dynamic Credit Investment in Partially Observed Markets

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite state Markov chain. We reduce the partially observed stochastic control problem to a complete observation risk sensitive control problem via the filtered regime switching probabilities. We separate the latter into pre-default and post-default dynamic optimization subproblems, and obtain two coupled Hamilton-Jacobi-Bellman (HJB) partial differential equations. We prove existence and uniqueness of a globally bounded classical solution to each HJB equation, and give the corresponding verification theorem. We provide a numerical analysis showing that the investor increases his holdings in stock as the filter probability of being in high growth regimes increases, and decreases his credit risk exposure when the filter probability of being in high default risk regimes gets larger

Pairs Trading under Drift Uncertainty and Risk Penalization

In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics. The relationship between pairs, called a spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time, finite-state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to the one with full information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under full and partial information and show that the certainty equivalence principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a toy example with a two-state Markov chain.Comment: 24 pages, 4 figure

Utility indifference pricing with market incompleteness

Utility indifference pricing and hedging theory is presented, showing how it leads to linear or to non-linear pricing rules for contingent claims. Convex duality is first used to derive probabilistic representations for exponential utility-based prices, in a general setting with locally bounded semi-martingale price processes. The indifference price for a finite number of claims gives a non-linear pricing rule, which reduces to a linear pricing rule as the number of claims tends to zero, resulting in the so-called marginal utility-based price of the claim. Applications to basis risk models with lognormal price processes, under full and partial information scenarios are then worked out in detail. In the full information case, a claim on a non-traded asset is priced and hedged using a correlated traded asset. The resulting hedge requires knowledge of the drift parameters of the asset price processes, which are very difficult to estimate with any precision. This leads naturally to a further application, a partial information problem, with the drift parameters assumed to be random variables whose values are revealed to the hedger in a Bayesian fashion via a filtering algorithm. The indifference price is given by the solution to a non-linear PDE, reducing to a linear PDE for the marginal price when the number of claims becomes infinitesimally small

Optimal investment and hedging under partial and inside information

This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time $0$ of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy

Optimal investment and hedging under partial and inside information

This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time $0$ of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy

Executive stock option exercise with full and partial information on a drift change point

We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration $\widehat{\mathbb{F}}$ in which the stock drift becomes a diffusion driven by the innovations process, an $\widehat{\mathbb{F}}$-Brownian motion also driving the stock under $\widehat{\mathbb{F}}$, and the partial information optimal stopping value function has two spatial dimensions. We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the fully informed agent can result in exercise patterns which exploit the information on the change point, lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance.Comment: 48 pages, final version, accepted for publication in SIAM Journal on Financial Mathematic