Using daily returns of the S&P 500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the probability of large portfolio losses. With more than 400 stocks to choose from, our study seems to be the first application of extreme value techniques in portfolio management on a large scale. The primary aim of our investigation is the potential of ERI in practice. The performance of this strategy is benchmarked against the minimum variance portfolio and the equally weighted portfolio. These fundamental strategies are important benchmarks for large-scale applications. Our comparison includes annualized portfolio returns, maximal drawdowns, transaction costs, portfolio concentration, and asset diversity in the portfolio. In addition to that we study the impact of an alternative tail index estimator. Our results show that the ERI strategy significantly outperforms both the minimum-variance portfolio and the equally weighted portfolio on assets with heavy tails. 1 c 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http: // creativecommons. org/ licenses/ by-nc-nd/ 4. 0/ arXiv:1505.04045v1 [q-fin.PM] 15 May 2015 2 c 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http: // creativecommons. org/ licenses/ by-nc-nd/ 4. 0/ In our paper we follow the basic line of developments on the optimization problem that the investment strategy is derived from. Our reformulation of 3 c 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http: // creativecommons. org/ licenses/ by-nc-nd/ 4. 0/ 5 c 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http: // creativecommons. org/ licenses/ by-nc-nd/ 4. 0/ 7 c 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http: // creativecommons. org/ licenses/ by-nc-nd/ 4. 0/
This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.
To cite this version:Georgi K. Mitov, Kosto V. Mitov, Nikolay M. Yanev. Critical randomly indexed branching processes. Statistics and Probability Letters, Elsevier, 2009, 79 (13) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPTCritical Randomly Indexed Branching Processes Abstract Bienaymé-Galton-Watson branching processes subordinated to a continuous time random index are considered. The branching processes are assumed to be critical with finite or infinite offspring variance. The indexing process is assumed to be a renewal one with finite or infinite mean of the interarrival times. Under these conditions we prove the asymptotic formulas for the first two moments and for the probability of non-extinction. We also obtain proper limiting distributions under suitable normalization.
Interpretative Decision No. 1/2013 of the Criminal College of the Supreme Court of Cassation stipulates that “… the court shall render a decision on the civil claim, accepted for joint consideration within the penal procedure, when, in the course of the first instance proceedings, before the verdict is pronounced, any of the grounds under Art. 79(1) of the Bulgarian Criminal Code occurs (death of the perpetrator, expiration of the term of limitation, amnesty)”. This decision of the Criminal College raises complex theoretical and practical questions related to the rules for hearing the civil claim, considering the criminal nature of the proceedings, the functions of the parties, the participation of the perpetrator’s inheritors (where the perpetrator has died), how their rights and legitimate interests will be guaranteed, and other questions that the Interpretative Decision failed to answer. Following an analysis of the established problems, a proposal for their solution is made through official referral of the civil claim to the civil court as to continue the court proceedings after the criminal case has been discontinued.
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