On application of risk measures in portfolio selection problems
Martin Jandačka
PhD thesis advisor: Daniel Ševčovič
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Summary: The dissertation thesis deals with risk and integration of risk to the portfolio selection problem. The goal of the dissertation thesis is to explore the influence of risk on investor's behavior. In first part we formalize the portfolio selection problem with risk constraint on the final infimum wealth of investor. We then analyse behavior of the investor under the presence of the risk constraint on a numerical example. In second part of the dissertation we integrate the risk generated by imperfect portfolio hedging and from the possibility of default of the counterparty, into the option pricing model. We numerically analyse the model and show its ability to explain volatility smile. We illustrate the problem of integrated versus separated analysis of credit and market risk and show when the separated analysis will not underestimate the overall risk. In the last part of the dissertation we focus on aggregation of time series models. We deal with the aggregation of time series over longer time horizon and with the choice of optimal data frequency. We analyse the aggregation of GARCH model and its conditional variance and kurtosis. We derive the limits behavior of conditional variance and kurtosis when the time horizon goes to infinity.
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[1] Breuer, T., Jandacka, M. (2007), Portfolio Selection with Transaction Costs under Expected Shortfall Constraints, Computational Management Science, Volume 5, 305-316

[2] Breuer, T., Jandacka.,M. (2007), Adverse Interrisk Diversification Effects for FX Forwards, Numerical Methods for Finance, 53-62, edited by Appleby, J.A.D, Edelman, D.C., Miller, J.J.H., Published by Chapman & Hall/CRC Financial Mathematics Series

[3] Breuer, T., Jandacka, M. (working paper), Temporal Aggregation of GARCH Models: Conditional Kurtosis and Optimal Frequency, ssrn.com/abstract=967824

[4] Breuer, T., Jandacka, M., Krenn. G. (working paper), Towards an Integrated Measurement of Credit and Market Risk, www.bis.org/bcbs/events/rtf05breuer.pdf

Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (2008), Compounding Effects between Market and Credit Risk: The Case of Variable-Rate Loans, Pillar II in the New Basel Accord, The Challenge of Economic Capital, 371- 384, edited by Resti, A., Risk Books

[4] Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (2008), Hedge the Stress: Using Stress Tests to Design Hedges of Foreign Currency Loans, Stresstesting for Financial Institutions, Applications, Regulations and Techniques, 111-126, edited by Rosch, D., Scheule, H., Risk Books

[5] Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (2009), How to Find Plausible, Sever, and Useful Stress Scenarios, International Journal of Central Banking, Volume 5, Number 3 (September 2009) 205-224

[6] Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (2008), Regulatory capital for market and credit risk integration: is current regulation always conservative?, Discussion Paper Series 2: Banking and financial Studies No 14/2008

[7] Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (working paper), InterRisk Diversification Effects of Integrated Market and Credit Risk Analysis, download

[8] Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (2008), Is Current Capital Regulation Based on Conservative Risk Assessment?, Summer Financial Stability Report 15, Oestereichische Nationalbank 2008, 112-118 download

[9] Breuer, T., Jandacka, M., Rheinberger, K., Summer, M. (forthcoming 2009), Does adding up of economic capital for market- and credit risk amount to coservative risk assessment?, Journal of Banking and Finance (forthcoming 2009)

[10] Jandacka, M.,Sevcovic, D. (2005), On the risk adjusted pricing methodology based valuation of vanilla options and explanation of the volatility smile, Journal of Applied Mathematics 3, 235-258 download