Light Stocks and Wealth Allocation

The aim of this paper is to deal with the problem of wealth allocation. We assume that an investor can share her/his money between consumption, riskless bonds, risky assets frequently traded in the market and illiquid stocks. The financial nature of thin stocks requires the description of their dynamics via jump processes, rather than continuous processes. Therefore, a stochastic control problem in a jump diffusion context is developed. In this paper the dynamic programming approach is adopted, and the optimal investment strategies are derived in closed form