Portfolio frontiers with restrictions to tracking error volatility and value at risk

Asset managers are often given the task of restricting their activity by keeping both the value at risk (VaR) and the tracking error volatility (TEV) under control. However, these constraints may be impossible to satisfy simultaneously because VaR is independent of the benchmark portfolio. The management of these restrictions is likely to affect portfolio performance and produces a wide variety of scenarios in the risk-return space. The aim of this paper is to analyse various interactions between portfolio frontiers when risk managers impose joint restrictions upon TEV and VaR. Specifically, we provide analytical solutions for all the intersections and we propose simple numerical methods when such solutions are not available. Finally, we introduce a new portfolio frontier.     

An optimal investment model with Markov-driven volatilities

We consider a multi-stock market model. The processes of stock prices are governed by stochastic differential equations with stock return rates and volatilities driven by a finite-state Markov process. Each volatility is also disturbed by a Brownian motion; more exactly, it follows a Markov-driven Ornstein–Uhlenbeck process. Investors can observe the stock prices only. Both the underlying Brownian motion and the Markov process are unobservable. We study a discretized version, which is a discrete-time hidden Markov process. The objective is to control trading at each time step to maximize an expected utility function of terminal wealth. Exploiting dynamic programming techniques, we derive an approximate optimal trading strategy that results in an expected utility function close to the optimal value function. Necessary filtering and forecasting techniques are developed to compute the near-optimal trading strategy.     

Optimal insurance contract and coverage levels under loss aversion utility preference

This study develops an optimal insurance contract endogenously and determines the optimal coverage levels with respect to deductible insurance, upper-limit insurance, and proportional coinsurance, and, by assuming that the insured has an S-shaped loss aversion utility, the insured would retain the enormous losses entirely. The representative optimal insurance form is the truncated deductible insurance, where the insured retains all losses once losses exceed a critical level and adopts a particular deductible otherwise. Additionally, the effects of the optimal coverage levels are also examined with respect to benchmark wealth and loss aversion coefficient. Moreover, the efficiencies among various insurances are compared via numerical analysis by assuming that the loss obeys a uniform or log-normal distribution. In addition to optimal insurance, deductible insurance is the most efficient if the benchmark wealth is small and upper-limit insurance if large. In the case of a uniform distribution that has an upper bound, deductible insurance and optimal insurance coincide if benchmark wealth is small. Conversely, deductible insurance is never optimal for an unbounded loss such as a log-normal distribution.