Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time $t_d$ during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone. In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of $t_d$, and tends to $0$ as time tends to $t_d^-$ with a speed that we can characterize. When the dividend function is linear in a neighbourhood of zero, then we show continuity of the exercise boundary and a high contact principle in the left-hand neighbourhood of $t_d$. When it is globally linear, then right-continuity of the boundary and the high contact principle are proved to hold globally. Finally, we show how all the previous results can be extended to multiple dividend payment dates in that case.

Approximation solutions for indifference pricing under general utility functions

With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners use: Best Estimate plus a "Market Value Margin". Furthermore, we compare our approximations to known analytical results for exponential and power utility

Symmetries in Jump-Diffusion Models with Applications in Option Pricing and Credit Risk

It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work it was shown that when invoked as a fundamental first principle, it provides a powerful alternative method for the derivation of prices and hedges of derivative securities, when prices of the underlying tradables are driven by Wiener processes. In this article we extend this work to the pricing problem in markets driven not only by Wiener processes but also by Poisson processes, i.e. jump-diffusion models. It is shown that in this case too, the focus on symmetry aspects of the problem leads to important simplifications of, and a deeper insight into the problem. Among the applications of the theory we consider the pricing of stock options in the presence of jumps, and Levy-processes. Next we show how the same theory, by restricting the number of jumps, can be used to model credit risk, leading to a `market model' of credit risk. Both the traditional Duffie- Singleton and Jarrow-Turnbull models can be described within this framework, but also more general models, which incorporate default correlation in a consistent way. As an application of this theory we look at the pricing of a credit default swap (CDS) and a first-to- default basket option.option pricing, jump diffusion, local scale invariance, homogeneity, partial differential difference equations

Politiek, cultuur, taal en religie. Een analyse van het stemgedrag tijdens het Eurovisie Songfestival

Een econometrische analyse van dertig jaar Eurovisie Songfestival werpt een nieuwe blik op de Europese verhoudingen. Zo hebben een aantal landen een duidelijke voorliefde voor liedjes die afkomstig zijn uit landen met dezelfde religie. Tegelijkertijd hebben veel landen een uitgesproken voorkeur voor de liedjes afkomstig van buurlanden en andere landen in hun nabijheid, zelfs na correctie voor overeenkomsten in taal en cultuur. Het ligt voor de hand dit te interpreteren als bewijs voor vriendjespolitiek. Echter, de veelgehoorde beschuldigen van politiek gekleurd stemgedrag aan het adres van een aantal landengroepen (zoals voormalig Joegoslavië, Scandinavië en Oost-Europa) worden in de meeste gevallen niet ondersteund door de data. Alleen tegen de Baltische staten is er overtuigend bewijs voor het bevoordelen van de wederzijdse liedjes

Plant Performance in Precision Horticulture: Optimal climate control under stochastic uncertainty

This paper presents a risk mitigating, time-varying feedback control algorithm for crop production when state dynamics are subject to uncertainty. The model based case study concerns a 40 day production round of lettuce in a greenhouse where control input consists of daily and nightly temperature set points. The control problem was formulated in terms of a stochastic Markov decision process with the objective to maximize the expected net revenue at harvest time. The importance of time-varying feedback and of risk mitigation was investigated by making a comparison with a controller that takes uncertainty into account but is static and a controller which is dynamic but ignores the uncertainty in the state dynamics. For the case of heat limited crop growth, and strict requirements on harvest weight precision, the dynamic stochastic controller outperformed the static controller in terms of both maximal expected net revenue (by 19 %) and state precision at harvest time (with 50 % less standard deviation). It also outperformed the deterministic controller for both criteria (15 % in maximal expected net revenue and 8 % less standard deviation). A detailed sensitivity analysis showed that such improvements in performance levels are robust, since they hold over large ranges of uncertainty in state dynamics, required harvest precision levels, starting days, and initial weights. The results provide insights in potential of dynamic feedback and risk mitigation strategies for high precision requirements under uncertainty. Although the results should be interpreted with caution, they illustrate the considerable potential benefit for stochastic greenhouse climate control under uncertainty when high precision is required

The optimal date to arrange a loan

Wie een lening moet afsluiten kan dat direct doen, of afwachtenin de hoop dat de rente zal dalen vóór het moment dat de leningecht nodig is. Maar als de rente niet daalt maar stijgt, wordt delening duurder. Dus wat is wijsheid?Wie een lening moet afsluiten kan dat direct doen, of afwachtenin de hoop dat de rente zal dalen vóór het moment dat de leningecht nodig is. Maar als de rente niet daalt maar stijgt, wordt delening duurder. Dus wat is wijsheid