SUMMARY This paper presents an analysis of the tracking problems of multiple indices with multidimensional performance criterion consisting of mean wealth and the tracking errors. We evaluate the performance of portfolios via the vector inequalities defined by convex cones, which enable us to...

We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has memory described by two parameters. For this market model,...

We present a general approach to the pricing of products in finance and insurance in the multi-period setting. It is a combination of the utility indifference pricing and optimal intertemporal risk allocation. We give a characterization of the optimal intertemporal risk allocation by a first...

In a jump-diffusion model of complete financial markets, we study the problem of minimizing the expectation of hedging loss weighted by power functions. We obtain the optimal portfolio by separating the problem into a hedging problem and an optimization problem.

The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete-time financial models with cone-constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super-hedging a contingent claim, which is...

We propose a long term portfolio management method which takes into account a liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian) control problem framework and then the optimal portfolio strategy hedges the liability by directly tracking a benchmark process which...

We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We give a sufficient condition for the binary model to be arbitrage-free. In a case when arbitrage opportunities exist, we present the rate...