Pricing and hedging in a single period market with random interval valued assets

• Published in: International journal of approximate reasoning Vol. 54; no. 9; pp. 1310 - 1321
• Main Author: You, Surong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.11.2013; Elsevier
• Subjects: Applied sciences; Approximation; Equivalence; Exact sciences and technology; Intervals; Markets; Operational research and scientific management; Operational research. Management science; Portfolio theory; Pricing; Random interval; Reasoning; Risk-neutral pricing measure; Robust arbitrage; Robust replicative strategy; Security; Strategy; Risk-neutral pricing measure; Random interval; Robust replicative strategy; Robust arbitrage; Arbitration; Warranty; Imprecise probability; Probabilistic approach; Set computation; Financial market; Market survey; Contingent asset; Economic market; Pricing; Robustness; Tariffication; Portfolio management; Derived product
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2013.06.002

In this article, a new financial market model, in which securities have random interval valued payoffs, is proposed. As an extension of traditional random market model, some concepts, such as robust arbitrage opportunities, risk-neutral pricing measures and robust replicative strategies, are given and discussed parallel to those in traditional market analysis. With these new concepts, problems of pricing and hedging are analyzed. It is shown that the requirement of no robust arbitrage opportunities is equivalent to the existence of risk-neutral pricing measures. Taking no robust arbitrage as the valuation principle, the problem of pricing a contingent claim with random interval valued payoff is discussed. All no robust arbitrage prices of the claim form an interval, whose endpoints can be got from the risk-neutral pricing measures or from robust replicative strategies. •Random intervals are used to model future uncertain payoffs of securities.•New concepts of robust arbitrage, risk-neutral pricing measure and robust replicative strategies are proposed for discussion in the new market model.•There exists no robust arbitrage opportunity, if and only if there is a risk-neutral pricing measure.•To a contingent claim, a price interval can be got based on no robust arbitrage argument.•The endpoints of the price interval of a contingent claim can also be represented by robust replicative strategies.