A multi-asset stochastic volatility model is presented. This is based on the Heston stochastic volatility model. It has the advantage of being sufficiently flexible to interpret the individual asset dynamics as well as the interdependencies among them, while still being analytically tractable. A formula for the joint transition probability density function of the stochastic process implicitly defined by the model is deduced. This formula is expressed as a one dimensional integral of an explicitly known function and allows us to derive elementary formulae for the conditional mean and variance of the asset price log-returns. A calibration procedure is proposed and tested on simulated data.

A stochastic model to describe the joint dynamics of financial market variables (i.e., equity market index, gross domestic product) and survival probability is proposed. The model is analytically tractable and may be used to price some mortality derivatives. A simulation study is carried out.

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This paper deals with the problem of determining "stable" portfolio allocations over a given time interval. Two portfolio optimization problems are formulated in the multi-asset Heston framework. The portfolio return is modeled by using a generalization of the Heston stochastic volatility model and explicit formuls for the conditional expected mean, the variance and the transition probability density function of the portfolio return process are deduced. These formuls are used to define the objective functions of the portfolio optimization problems. The optimal Pareto sets of these problems are explored to determine allocations which belong to the optimal Pareto sets of both optimization problems and that belong to these sets over a time interval. An experiment on real data is proposed to illustrate the implications of the "stable" asset allocation.