On the investment-consumption model with transaction costs

Projet META2This paper considers the optimal consumption and investment policy for an investor who has avaible one bank account paying a fixed interest rate r and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional tothe size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality is solved, by using a numerical algorithm based on policies iterations and multigrid methods. Numerical results are displayed for n =1 and n =2

Large Deviations for the Stochastic Shell Model of Turbulence

In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for so- lutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell-Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc.Comment: 21 pages, submitted for publicatio