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Essays on the Applications of Conditional Expectation in Finance and Insurance

Monday, 27 May, 2013 - 09:45
Campus: Brussels Humanities, Sciences & Engineering campus
Faculty: Social Sciences and Solvay Business School
E
0.10
Jing Yao
phd defence

The public defence of the Ph.D. in Economics for Jing Yao will take place on Monday May 27th 2013 at 11am on the Etterbeek-campus of the Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels in Building E, level 0, room E.0.10. The Ph.D thesis is called ‘Essays on the Applications of Conditional Expectation in Finance and Insurance.’

Promoter: Prof. dr. Steven Vanduffel

Abstract

Academic economists use techniques from the fields of probability and statistics to assess or to calculate risk in the context of finance and actuarial science. The conditional expectation has always played a fundamental role in these fields. In this dissertation, we study three applications of the conditional expectation. We first employ the conditional expectation to provide a shorter and more elegant proof of Stein's Lemma for the elliptical random vectors. We also study several new applications. In our second topic, we derive model-independent lower bounds for Asian options under the stop-loss order in a rather general market setting. We also show that these bounds can be used as control variates to significantly improve the efficiency of Monte Carlo simulation. Inspired by the idea of conditioning, we proceed to propose a semi-analytic pricing method that employs a two-step approach for pricing Asian options in a Lévy market. Other applications are also discussed. The third topic focuses on the sum of the dependent random variables that are generalized Gamma distributed. We derive several convex lower bounds and compare our results to the moment matching method. Furthermore, we apply our approach to solving capital allocation problems and to improving Monte Carlo simulation. At the end of the dissertation we also present a discussion on a paper of Zhu and Li (2012). Specifically, we show how a proof for a key result in their paper can be greatly simplified by conditioning first.

Attachment: 
PDF icon Yao_abstract.pdf