# This is my personal web page

My name is Karel Janecek, e-mail karel@janecek.name.

I completed my Ph.D. at the Mathematical Finance program at
Carnegie Mellon University in summmer 2004. Afterwards I worked as a research scientist in Financial Mathematics
at the
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences. Since summer 2005 I have worked full time at the propriatory trading investment house RSJ Invest, a.s. , where I am a member of the Board of Directors.

RSJ Invest, a.s.

Wratislavsky palac, Trziste 13

118 00 Prague 1

Czech Republic

Phone: +420 25753 1234

Fax: +420 25753 0645

E-mail: karel.janecek@rsj.cz

RSJ Invest, a.s. is a member of the Euronext.LIFFE (London International Futures and Options Exchange). The company serves as a Designated Market Maker (DMM) for the short-term interest rate (STIR) futures contracts.

RSJ Invest is the largest propriatory trader on the derivative exchange, trading around 4% of the entire exchange volume. The trading volume of RSJ Invest exceeds 2 million lots per month.

## Research

### Asymptotic analysis for optimal investment under transaction costs

My current research interests include the expected utility maximization under transaction costs. Recently I
obtained an explicit asymptotic formula for the loss in value function for small transaction
costs. This has been an open question until now, even though the results are of major importance for practical
portfolio management and hedging applications.

The paper is a joint work with prof. S.E. Shreve. It was published in Finance and Stochastics(8), 2004.

You can download the paper Asymptotic Analysis for Optimal Investment
and Consumption with Transaction costs in pdf format.
### Analysis of reasonable risk aversion of real world individual investors.

As an author of an analysis software for the casino game of blackjack (see for example the Statistical Blackjack Analyzer web page.) I have first hand access to reasonable usage of risk aversion by professional blackjack players. It was a surprise for me to learn, after coming to CMU, that most theoretical economists assume very low, and I would argue unrealistically low, aversion to risk for individual investors. In my paper I perform the analysis of risk aversion and argue that the standard economic assumptions may be incorrect. Namely, by accepting what I consider to be reasonable aversion to risk for individual investors, several economic puzzles can be explained. I argue that the *equity premium puzzle* can be explained, as can be the *low participation rate in the stock market*, or the size of the *risk free rate*.
You can download the working paper What is a realistic aversion to risk for real-world individual investors? in pdf format.

### Analysis of the size of equilibrium risk free rate.

The section about risk free rate puzzle from the previous paper appears to be of
major significance. I made an extra note devoted to the analysis of the size of risk free rate, given the plausible assumption of high risk aversion of individual investors. The paper points out the fact that for reasonable values of risk aversion parameter, the size of risk free rate is not an increasing function of risk aversion, and the low risk free rate and high equity premium are not in contradiction. The main reason is that the effect of *precautionary savings* may be significant.
You can download the working paper The low risk free rate is not too low in pdf format.