2 resultados para reversible jump MCMC

em Université de Lausanne, Switzerland


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A 98-year-old woman was referred to our hospital because of myoclonia. The concentration of calcium and vitamin D in the serum was low. In this context, we concluded of neuromuscular irritability secondary to hypocalcaemia. The symptoms disappeared after a treatment of intravenous calcium. This case shows how important it is to investigate electrolytes in case of neuromuscular irritability symptoms in elderly people.

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The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.