Risk-sensitive investment in a finite-factor model

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner and Lipster (2014) is used to prove the martingale property of the relevant density processes.Comment: 23 pages, 1 figur

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

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.

Optimal Asset Allocation in a High Inflation Regime: a Leverage-feasible Neural Network Approach

We study the optimal multi-period asset allocation problem with leverage constraints in a persistent, high-inflation environment. Based on filtered high-inflation regimes, we discover that a portfolio containing an equal-weighted stock index partially stochastically dominates a portfolio containing a capitalization-weighted stock index. Assuming the asset prices follow the jump diffusion model during high inflation periods, we establish a closed-form solution for the optimal strategy that outperforms a passive strategy under the cumulative quadratic tracking difference (CD) objective. The closed-form solution provides insights but requires unrealistic constraints. To obtain strategies under more practical considerations, we consider a constrained optimal control problem with bounded leverage. To solve this optimal control problem, we propose a novel leverage-feasible neural network (LFNN) model that approximates the optimal control directly. The LFNN model avoids high-dimensional evaluation of the conditional expectation (common in dynamic programming (DP) approaches). We establish mathematically that the LFNN approximation can yield a solution that is arbitrarily close to the solution of the original optimal control problem with bounded leverage. Numerical experiments show that the LFNN model achieves comparable performance to the closed-form solution on simulated data. We apply the LFNN approach to a four-asset investment scenario with bootstrap resampled asset returns. The LFNN strategy consistently outperforms the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the terminal date. These results suggest that during persistent inflation regimes, investors should favor short-term bonds over long-term bonds, and the equal-weighted stock index over the cap-weighted stock index

Modelling FX smile : from stochastic volatility to skewness

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