The variational principle states that if a differentiable functional F attains its minimum at some point zi, then Fâ€™(C) = 0; it has proved a valuable tool for studying partial differential equations.â€¦ (More)

I. The central result. The grandfather of it all is the celebrated 1961 theorem of Bishop and Phelps (see [7], [8]) that the set of continuous linear functionals on a Banach space E which attainâ€¦ (More)

December 8, 2008 Abstract. In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of theâ€¦ (More)

This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with nonconstant discounting. The equilibrium equation takes twoâ€¦ (More)

As coastal fisheries around the world have collapsed, industrial fishing has spread seaward and deeper in pursuit of the last economically attractive concentrations of fishable biomass. For aâ€¦ (More)

Given a multi-dimensional Markov diffusion X, the Malliavin integration by parts formula provides a family of representations of the conditional expectation E[g(X2)|X1]. The different representationsâ€¦ (More)

This paper considers the portfolio management problem for an investor with finite time horizon who is allowed to consume and take out life insurance. Natural assumptions, such as different discountâ€¦ (More)