Titlebook: Introduction to Stochastic Finance; Jia-An Yan Textbook 2018 Springer Nature Singapore Pte Ltd. and Science Press 2018 portfolio selection

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Stochastic Calculus and Semimartingale Model, developed a modern theory of martingales, the general theory of stochastic processes, and stochastic calculus on semimartingales. It turned out soon that semimartingales constitute the largest class of right continuous adapted integrators with respect to which stochastic integrals of simple predict

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Optimal Investment in Incomplete Markets,es. In a continuous-time model, the problem was studied for the first time by Merton (1969, 1971), who derived the Bellman equation for the value function of the optimization problem with the method of stochastic control. This method, however, requires the state processes to be Markovian. The martin

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Martingale Method for Utility Maximization,Karatzas (1989). The same problem in incomplete markets has been extensively studied by Karatzas et al. (1991). They judiciously augmented the stocks with fictitious ones to create a complete market, such that the fictitious stocks are superfluous in the optimal portfolio for the completed market. I

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Optimal Growth Portfolios and Option Pricing, out expressions of “optimal growth portfolios” in a geometric Lévy process model and a jump-diffusion-like process model. In Sect. 14.2, we present the “numeraire portfolio approach” to contingent claim pricing in a geometric Lévy process model. In Sect. 14.3 we give an overview of other martingale

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0172-5939 s general theory of static risk measures, basic concepts andThis book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected ut

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Optimal Investment-Consumption Strategies in Diffusion Models,itions, they proved that one can wisely choose virtual stocks, such that in the resulting optimal portfolio for the solution to utility maximization problem in the completed market, virtual stocks are superfluous. Thus, this solution is also the optimal one in the original incomplete market.