## Contributed Session Thu.3.H 3021

#### Thursday, 15:15 - 16:45 h, Room: H 3021

**Cluster 7: Finance & economics** [...]

### Modern portfolio optimization

**Chair: Eligius M.t. Hendrix**

**Thursday, 15:15 - 15:40 h, Room: H 3021, Talk 1**

**Süleyman Özekici**

Portfolio selection with hyperexponential utility functions

**Coauthor: Turan Bulmuş**

**Abstract:**

We analyze a single-period portfolio selection problem where the investor maximizes the expected utility of the terminal wealth. The utility function is hyperexponential. This is due to the fact that the risk tolerance of the investor at the end of the period when the terminal wealth is realized depends on the random state of the market at that time. This setting is also applicable in cases where an investment consultant is not sure about the risk profile of a client. It is well-known that an investor is memoryless in wealth for exponential utility functions with some known risk tolerance. In other words, the investment portfolio consisting of risky stocks does not depend on the level of wealth. However, we show that this is no longer true if the utility function is hyperexponential. We also obtain a number of interesting characterizations on the structure of the optimal policy.

**Thursday, 15:45 - 16:10 h, Room: H 3021, Talk 2**

**Eligius M.t. Hendrix**

On finding optimal portfolios with risky assets

**Coauthors: Leocadio G. Casado, Juan Francisco R. Herrera, Michiel Janssen**

**Abstract:**

Since the introductory work of Markowitz, the questions of finding optimal portfolios in order to maximise return and minimise risk, have been made explicit in terms of optimisation models. As long as returns are described by normal distributions, analytical expressions can be derived for finding optimal portfolio weights. The optimal mix is more difficult to find when we are dealing with so-called fat tails. This means that probabilities on extreme outcomes are typically higher than in the normal distribution, thus providing a challenge for the composition of low risk portfolios. A general way to do so is to combine simulation of rare events with optimization tools. In this context, a specific weight adjusting algorithm is described and compared to the use of standard nonlinear optimization solving an equivalent problem.

% This work has been supported by grants from the Spanish Ministry of Science and Innovation (TIN2008-01117) and Junta de Andalucía (P11-TIC-7176), in part financed by the European Regional Development Fund (ERDF).