5 We present efficient partial differential equation (PDE) methods for continuous time mean6 variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. 7 The standard formulation of mean-variance optimal portfolio allocation problems, where the 8 total wealth is the underlying stochastic process, gives rise to a one-dimensional (1-D) non-linear 9 Hamilton-J...

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the common noise that all agents are exposed to, whereas idiosyncratic randomness can be eliminated by an Exact Law of Large Numbers. Under a structu...

In this paper we investigate portfolios consisting of instruments whose logarithms are mean-reverting. Under the assumption that portfolios are constant, we derive analytic expressions for the expected wealth and the quantile-based risk measure capital at risk. Assuming that short-selling and borrowing is allowed, we then solve the problems of global minimum capital at risk, and problem of find...

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dy...

This paper studies capital allocation problem based on minimizing loss functions. Two capital allocation models based on the Mean-Variance principle are proposed. General formulas for optimal capital allocations for both models are derived according to quadratic distance measure. In particular, we discuss centrally symmetric distributions and gamma distributions. Some numerical examples are giv...

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