Toward the theory of pricing of options of both European and American types. I: Discrete time. (English. Russian original) Zbl 0833.60064

Theory Probab. Appl. 39, No. 1, 14-60 (1994); translation from Teor. Veroyatn. Primen. 39, No. 1, 23-79 (1994).
From the authors’ summary: The article consists of two parts (part I discrete and part II continuous time). Its aim is a presentation of basic notions, problems and results of financial mathematics related to pricing of options or contracts with options. In this part I, it is assumed that those contracts are concluded on a discrete stock market \((B,S)\) with two actives: a riskless bank account \(B = (B_n)_{n \geq 0}\) and a risk share \(S= (S_n)_{n \geq 0}\). Options of European as well as US types are considered. Special attention is paid to martingale pricing methods for hedge strategies with concrete applications to call and put options. [For part II see below].
Reviewer: M.Jerschow (Essen)


60H30 Applications of stochastic analysis (to PDEs, etc.)
91G20 Derivative securities (option pricing, hedging, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory


Zbl 0833.60065