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Optimal RiskSharing with Effort and Project
 Choice”, Journal of Economic Theory
"... We consider firstbest risksharing 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 optiontype payoff, where the ..."
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We consider firstbest risksharing 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 optiontype 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 forwardbackward 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 forwardbackward 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 MEANVARIANCE PREFERENCES
, 2006
"... We consider a complete financial market with deterministic parameters where an investor and a fund manager have meanvariance preferences. The investor is allowed to borrow with riskfree 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 meanvariance preferences. The investor is allowed to borrow with riskfree rate and dynamically allocate his wealth in the fund provided his holdings stay nonnegative. The manager gets proportional fees instantaneously for her management 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 numerical solution of a nonlinear equation and is not unique in general. In onedimensional 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 Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction and