Download PDF by Jacques Janssen (auth.), Jacques Janssen, Christos H.: Advances in Stochastic Modelling and Data Analysis

By Jacques Janssen (auth.), Jacques Janssen, Christos H. Skiadas, Constantin Zopounidis (eds.)

ISBN-10: 9048145740

ISBN-13: 9789048145744

ISBN-10: 9401706638

ISBN-13: 9789401706636

Advances in Stochastic Modelling and knowledge Analysis provides the newest advancements within the box, including their purposes, commonly within the components of assurance, finance, forecasting and advertising and marketing. additionally, the prospective interactions among info research, synthetic intelligence, choice aid platforms and multicriteria research are tested by means of most sensible researchers.
Audience: a large readership drawn from theoretical and utilized mathematicians, resembling operations researchers, administration scientists, statisticians, computing device scientists, bankers, advertising and marketing managers, forecasters, and medical societies equivalent to EURO and TIMS.

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IL Investors such as insurance companies or pension funds have future liabilities and keep reserves in bonds. They face the risk of multiperiod interest rate changes and plan to buy bonds according to their estimations of future liabilities and interest rates. We use a discrete time model and show that the choice of the length of the bonds bought or sold determines a kinked payoff function. For investors who adopt a mean-variance strategy, hedging may be a common solution. By using a dynamic programming mode 1 we find that in every period investors may choose to hedge for the next period.

Moreover, this framework is quite general since it enables market participants to consume as well as invest. Thus, permitting a unified approach to the problems of: option pricing, consumption and investment, and equilibrium in a financial market. Our main financial result is that (for a perpetual, dividendpaying American call option) the optimal exercise time is the ratio of the stopping boundary (b) to the drift of the transformed stock price process. Here, b equals the product of the inverse of the stock volatility times the log of the ratio of the optimal exercise stock price to the initial (time zero) stock price.

19). 3. 2) (where TbAt=min{Tb,t}), since V[(Tb A t)] t>Tb. B(O) - 80] =E[exp(O)], so E[V(O)] = 1. 2, we know that: E[V(O)] = E[V(Tb)]. 4), we conclude that: 1 =E[V(O)] =E[V(Tb)] =E[(Tb A t)]. 4. 6) 00 where the limit can be taken under the expectation operator since {V(Tb A t)} is hypothesized to be uniformly integrable and, thus, Theorem 5 of Shiryayev (1984, p. 187) can be invoked. Also, 49 (A7) since V(Tb A t) = V(Tb) whenever TbTb. b. 1. B(t)- et}, where e (A9) =AJl + A. CJ /2, and A.

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Advances in Stochastic Modelling and Data Analysis by Jacques Janssen (auth.), Jacques Janssen, Christos H. Skiadas, Constantin Zopounidis (eds.)


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