A stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation

Abstract

We present a new approach to asset allocation with transaction costs. A multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk. Utilizing portfolio protection and dynamic hedging, an investment portfolio similar to an option-like payoff structure on the initial investment portfolio is characterized. The relative changes in the expected terminal wealth, worst case payoff, and risk aversion, are studied theoretically and illustrated using a numerical example. This model dominates a static mean-variance model when the optimal portfolios are evaluated by the Sharpe ratio.

Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach

“…After obtaining the optimal x * 1 (z) and x * 2 (z), we can recover the optimal θ * , ϕ * , ϑ * , ψ * through normalization to give the solution to the above optimization problem (35). In particular, ϕ * and ψ * satisfy the third and the fourth constraints in (34).…”

“…Let θ * k (s), ϕ * k (s, z), ϑ * k (s) and ψ * k (s, z), k = 1, ..n − d, denote the optimal solution to the problem (35). By (32) in the proof of Lemma 3,…”

“…The present paper is different from these mentioned studies either in mathe-matical models or in methodologies. For other related literature, we refer to Pennanen [29] regarding duality approach, Zhao and Ziemba [35] regarding asset allocation with transaction costs; etc.…”

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

“…where U(AE) is a standard utility function, W is the portfolio value at the end of the horizon, and K is the portfolio's worst case outcome; see Zhao and Ziemba (2001) for a discussion of this approach. This objective function applies explicit downside loss control while maximizing the expected utility of wealth.…”

Portfolio Risk Management: Market Neutrality, Catastrophic Risk, and Fundamental Strength

“…The first formal axiomatic treatment of utility was given by von Neumann & Morgenstern (1991). Other objective functions are possible, such as the one proposed by Zhao & Zeimba (2001). The relative merits of using Markowitz mean-variance type models and those that trade off mean with downside semi-deviation are examined in Ogryczak & Ruszczynski (1999).…”