# Abstracts

**Consumption-Leisure-Investment Strategies with Time-Inconsistent Preference in a Life-Cycle Model**

*Qian Zhao (Macquarie University, Australia)*

Thursday June 5, 11:30-12:00 | session 7.2 | Portfolio Optimization | room CD

This paper aims at investigating a consumption-leisure-investment problem, where the object of an economic agent is to maximize the expected value of discounted lifetime utility in a life-cycle model. The agent is allowed to have considerable labor flexibility and the date of retirement is fixed. To incorporate some well-documented behavioral features of human beings, we consider the situation where the discounting is non-exponential. This situation is far from trivial and renders the optimization problem of the agent to be a non-standard one, namely, a time-inconsistent stochastic control problem. The extended HJB equation for the time-inconsistent control problem is given. A verification theorem is proved for a general discount function and a general utility function. Explicit-form solutions are presented for the logarithmic utility with the exponential discounting, the pseudo-exponential discounting and hyperbolic discounting.

**Dynamic Programming Equations for Portfolio Optimization under Partial Information with Expert Opinions**

*Ralf Wunderlich (Brandenburg University of Technology, Germany)*

Thursday June 5, 12:00-12:30 | session 7.2 | Portfolio Optimization | room CD

We investigate optimal portfolio strategies for utility maximizing investors in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at random discrete time points. These signals we model by a marked point process with jump-size distribution depending on the current state of the hidden Markov chain.

We use stochastic filtering to transform the original problem into an optimization problem under full information where the state variable is the filter for the Markov chain. The dynamic programming equation for this problem is studied with viscosity-solution techniques and with regularization arguments. For the case of power utility we present results from the numerical solution of the dynamic programming equation.

The talk is based on the following publications:

Frey, R., Gabih, A. and Wunderlich, R. (2012): Portfolio optimization under partial information with expert opinions. International Journal of Theoretical and Applied Finance, 15, No. 1.

Frey, R. and Wunderlich, R. (2013). Dynamic Programming Equations for Portfolio Optimization under Partial Information with Expert Opinions, arXiv:1303.2513.

**Robust Portfolio Choice and Indi fference Valuation**

*Roger Laeven (University of Amsterdam, The Netherlands)*

Thursday June 5, 12:30-13:00 | session 7.2 | Portfolio Optimization | room CD

We solve, theoretically and numerically, the problems of optimal portfolio choice and indifference valuation in a general continuous-time setting. The setting features (i) ambiguity and time-consistent ambiguity averse preferences, (ii) discontinuities in the asset price processes, with a general and possibly in finite activity jump part next to a continuous di ffusion part, and (iii) general and possibly non-convex trading constraints. We characterize our solutions as solutions to Backward Stochastic Differential Equations (BSDEs). Generalizing Kobylanski's result for quadratic BSDEs to an infi nite activity jump setting, we prove existence and uniqueness of the solution to a general class of BSDEs, encompassing the solutions to our portfolio choice and valuation problems as special cases. We provide an explicit decomposition of the excess return on an asset into a risk premium and an ambiguity premium, and a further decomposition into a piece stemming from the di ffusion part and a piece stemming from the jump part. We further compute our solutions in a few examples by numerically solving the corresponding BSDEs using regression techniques.