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Application of malliavin calculus to the portfolio theory

Krajna L.

Prace Naukowe Instytutu Matematyki Politechniki Wrocławskiej. Konferencje

2001

Vol. 24, nr 3

67-75

We present general solutions of portfolio optimization problems received for a huge subclass of diffusion models of financial markets with stochastic coefficients, defined by systems of stochastic differential equation. The idea of proposed methodology is based on the application of stochastic variational calculus to the construction of replicating portfolios (see also [6]). Derived closed formula for optimal portfolios beside traditional mean-variance optimization factor (see Markovitz Theory) also include intertemporal hedging factors which were postulated by Merton as early as in the 70s. Received results help to better understand the role of stochastic volatility and other stochastic parameters of the financial market model. Computer experiments allow to describe quantitatively the dynamics of optimal portfolios as well as the importance of all factors.