Past Mathematical Finance Seminar

A trader in finance is called an insider if she (or he) knows more about the prices in the market than can be obtained from the market history itself. This is the case if, for example, the trader knows something about the future price/value of a stock. We discuss the following question: What is the optimal portfolio of an insider who wants to maximize her expected profit at a given future time? The problem is that heavy trading by the insider will reveal parts of her inside price information to the market and thereby reduce her information advantage.

We will solve this problem by presenting a general anticipative stochastic calculus model for insider trading. Our results generalize equilibrium results due to Kyle (1985) and Back (1992).

The presentation is partly based on recent joint work with Knut Aase and Terje Bjuland, both at the Norwegian School of Economics and Business Administration (NHH).

In this paper we derive a stochastic partial di¤erential equation whose solutions are processes relevant to the portfolio choice problem. The mar- ket is incomplete and asset prices are modelled as Ito processes. We provide solutions of the SPDE for various choices of its volatility coe¢ - cient. We also show how to imbed the classical Merton problem into our framework.

We discuss recent advances in the probabilistic analysis of financial risk and uncertainty, including risk measures and their dynamics, robust portfolio choice, and some asymptotic results involving large deviations