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Optimal Risk-Sharing with Effort and Project
- Choice”, Journal of Economic Theory
"... We consider first-best risk-sharing problems in which “the agent ” can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the ..."
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We consider first-best risk-sharing problems in which “the agent ” can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the functional form of the option is obtained as a solution to an ordinary differential equation. In the general case, the optimal contract is a fixed point of a functional that connects the agent’s and the principal’s maximization problems. We apply martingale/duality methods familiar from optimal consumptioninvestment problems.
Maximum principle for optimal control of fully coupled forwardbackward stochastic differential delayed equations
- ESAIM: Control, Optimisation and Calculus of Variations
"... Abstract. This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient doe ..."
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Abstract. This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic control problems are discussed and both optimal controls are derived explicitly.
DELEGATED DYNAMIC PORTFOLIO MANAGEMENT UNDER MEAN-VARIANCE PREFERENCES
, 2006
"... We consider a complete financial market with deterministic parameters where an investor and a fund manager have mean-variance preferences. The investor is allowed to borrow with risk-free rate and dynamically allocate his wealth in the fund provided his holdings stay nonnegative. The manager gets pr ..."
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We consider a complete financial market with deterministic parameters where an investor and a fund manager have mean-variance preferences. The investor is allowed to borrow with risk-free rate and dynamically allocate his wealth in the fund provided his holdings stay nonnegative. The manager gets proportional fees instantaneously for her manage-ment services. We show that the manager can eliminate all her risk, at least in the constant coefficients case. Her own portfolio is a proportion of the amount the investor holds in the fund. The equilibrium optimal strategies are independent of the fee rate although the portfolio of each agent depends on it. An optimal fund weight is obtained by the numer-ical solution of a nonlinear equation and is not unique in general. In one-dimensional case, the investor’s risk is inversely proportional to the weight of the risky asset in the fund. We also generalize the problem to the case of multiple managers and provide some examples. Copyright © 2006 Coskun Cetin. This is an open access article distributed under the Cre-ative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction and
