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A review of margrabe formula and its applications in derivative pricing
No full textThis brief survey aims to reviews the Margrabe formula and its applications in derivative pricing. In particular, we examine financial products as asian options, corporate bonds and interest rate spread options
Underperformance fees and manager’s portfolio risk taking
No full textThis paper investigates how a manager’s compensation contract where good performance are rewarded and poor performance are penalized impacts on the managerial risk taking propensity. The results of the model indicates that the presence of underperformance penalty has a strong impact on the manager’s investment strategies. As the asset value goes to zero, the optimal proportional portfolio goes to infinity. On the other hand, as the asset value goes to infinity, the optimal proportional portfolio converges to the Merton constant, that is the portfolio the manager chooses if he were trading his own account. In some situations, the manager’s optimal portfolio is below the Merton constant. If the asset value is somewhat below the overperformance region, the manager chooses trading strategies more risky than the Merton constant. Thus, in order to assure that his incentive option will finish in-the-money, the manager increases the investment volatility, but not in the indiscriminate manner as he does in case of absence of underperformance penalty
Optimal annuitization and bequest motives
No full textTiming the annuitization decision has important economic implications because it has
a direct effect on how well prepared individuals are to provide consumptions in their old
age. It depends on several risk factors such as market risk, longevity risk, potential future
needs of liquid fund and bequest motives. Since the seminal contribution of Yaari (1965),
who showed that individuals with no bequest motive should convert all their retirement
wealth into annuities, a number of papers have analysed the annuitization decision under
the so-called all or nothing institutional arrangement, where immediate lifetime annuities
are purchased just at a one point in time. In this paper we investigate the effect of bequest
motivesontheannuitizationdecisionforaretiredindividualwhomaximizesthemarketvalue
of future cash-flows. From a mathematical point of view the problem is formulated as an
optimalstoppingproblem. Byusingthegeometricapproachtooptimalstoppingproblemfor
one-dimensional diffusion developed by Dayanik and Karatzas in [6], we determine explicitly
the value function as well as the optimal stopping time. Finally, we present numerical
examples comparing the optimal annuitization time with and without bequest motives
Optimal timing of the annuity purchase: Combined stochastic control and optimal stopping problem
No full textThe paper examines the optimal annuitization time and the optimal consumption/investment strategies for a retired individual subject to a constant force of mortality in an all-or-nothing framework. We allow for a different utility of consumption before and after annuitization. For a general family of preferences we characterize the value function and the optimal controls of the resulting combined stochastic control and optimal stopping problem. Assuming power utility functions we obtain explicit solutions. We show that if the individual evaluates the consumption flow and the annuity payments stream in the same way, then, depending on the parameters of the economy, the annuity is purchased at retirement or never. In the case when the individual is more risk averse in the annuity assessment, it is optimal to defer the annuitization until her wealth reaches a threshold, and such threshold depends on the arameters of the economy
Optimal timing of the annuity purchases: a combined stochastic control and optimal stopping problem
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