The Tail that Wags the Dog: Integrating Credit Risk in Asset Portfolios

Tails are of paramount importance in shaping the risk profile of portfolios with credit risk sensitive securities. In this context risk management tools require simulations that accurately capture the tails, and optimization models that limit tail effects. Ignoring the tails in the simulation or using inadequate optimization metrics can have significant effects and destroy portfolio efficiency. The resulting portfolio risk profile can be grossly misrepresented when long run performance is optimized without consideration of the short term tail effects. This paper illustrates the pitfalls and suggests models for avoiding them.

Long time asymptotics for optimal investment

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control pro\-blems, that we solve by duality method leading to ergodic risk-sensitive portfolio optimization problems. Special emphasis is placed on linear factor models where explicit solutions are obtained

Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is to show that the risk-sensitive jump diffusion problem can be fully characterized in terms of a parabolic Hamilton-Jacobi-Bellman PDE rather than a PIDE, and that this PDE admits a classical C^{1,2} solution.Comment: 33 page

Sufficient stochastic maximum principle for the optimal control of semi-Markov modulated jump-diffusion with application to Financial optimization

The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article we provide a sufficient stochastic maximum principle for the optimal control of a semi-Markov modulated jump-diffusion process in which the drift, diffusion and the jump kernel of the jump-diffusion process is modulated by a semi-Markov process. We also connect the sufficient stochastic maximum principle with the dynamic programming equation. We apply our results to finite horizon risk-sensitive control portfolio optimization problem and to a quadratic loss minimization problem.Comment: Forthcoming in Stochastic Analysis and Application

Long run risk sensitive portfolio with general factors

In the paper portfolio optimization over long run risk sensitive criterion is considered. It is assumed that economic factors which stimulate asset prices are ergodic but non necessarily uniformly ergodic. Solution to suitable Bellman equation using local span contraction with weighted norms is shown. The form of optimal strategy is presented and examples of market models satisfying imposed assumptions are shown

Socially responsible investment portfolios: does the optimization process matter?

This study investigates the impact of the choice of optimization technique when constructing Socially Responsible Investment (SRI) portfolios. Corporate Social Performance (CSP) scores are price sensitive information that is subject to considerable estimation risk. Therefore, uncertainty in the input parameters is greater for SRI portfolios than conventional portfolios, and this affects the selection of the appropriate optimization method. We form SRI portfolios based on six different approaches and compare their performance along the dimensions of risk, risk-return trade-off, diversification and stability. Our results for SRI portfolios contradict those of the conventional portfolio optimization literature. We find that the more “formal” optimization approaches (Black-Litterman, Markowitz and robust estimation) lead to SRI portfolios that are both less risky and have superior risk-return trade-offs than do more simplistic approaches; although they also have more unstable asset allocations and lower diversification. Our conclusions are robust to a series of tests, including the use of different estimation windows and stricter screening criteria