报告题目：Arbitrage-Free Derivatives Pricing in Nonlinear Markets

报 告  人：Prof. MarekRutkowski (悉尼大学)

报告时间：2016年11月3日下午

报告地点：知新楼B1238室

摘要：We study arbitrage-free pricing offinancial derivatives in the presence of funding costs, the counterparty creditrisk and market frictions affecting the trading mechanism, such ascollateralization and capital requirements. We extend in several respects the nonlinearpricing approach developed in El Karoui and Quenez (1997) and El Karoui et al.(1997).  The issues of the existence ofarbitrage opportunities for the hedger and for the trading desk in a nonlineartrading framework are examined. We introduce the concept of no-arbitrage withrespect to the null contract and a stronger notion of no-arbitrage for thetrading desk. We then proceed to the issue of unilateral fair valuation of agiven contract by the hedger endowed with an initial capital. A link betweenthe concept of no-arbitrage for the trading desk and the financial viability ofprices computed by the hedger is examined. Next, we introduce and analyze theconcept of a regular market model, which extends the concept of a non-linear pricingsystem in El Karoui and Quenez (1997). The goal is to identify a class ofmodels, which are arbitrage-free for the hedger and, in addition, have thedesirable property that for contracts that can be replicated, the replicationcost is also the fair price for the hedger. Finally, we discuss the BSDEapproach to the valuation and hedging of contracts in a model with differentialfunding rates, the counterparty risk and trading adjustments and illustratethis approach using also results from Dumitrescu et al. (2015).

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