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\title{Optimal Investment with Derivative Securities}
\author{Ronnie Sircar \\
  Princeton University}
\date{Computational Finance Seminar, \\
  November 8}


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\begin{abstract}
  We study the problem of portfolio optimization in an incomplete
  market using derivatives as well as basic assets such as stocks.  In
  such markets, an investor may want to use derivatives, as a proxy
  for trading volatility, for instance, but they should be traded
  statically, or relatively infrequently, compared with assumed
  continuous trading of stocks, because of the much larger transaction
  costs. We discuss the computational tractability obtained by
  assuming exponential utility, and the relation of the optimal
  strategy to the method of utility-indifference pricing. In
  particular, we show that the optimal number of derivatives to invest
  in is given by the Legendre transform of the indifference price as a
  function of quantity, evaluated at the market price.  Within popular
  diffusion stochastic volatility models, we discuss computational
  approaches for the associated quasilinear indifference pricing PDE.
  
  Joint work with A. Ilhan and M. Jonsson.

\end{abstract}


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