An application of the N-strip method of integral relations for analyzing the flow around a circular cone

The solution of sets of non-linear partial differential equations using the method of integral relations is considered. Emphasis is laid on the derivation of a general N-strip approximation algorithm. In order to check the applicability of this algorithm a program has been written to obtain the solution of the flow field around a circular cone at incidence in supersonic flow. Using the method of Stone, the angle of attack has been taken into account up to the second order. Thus a comparison can be made with the results given by Kopal.\ud \ud The results show that the N-strip algorithm in the case studied is a very attractive method which leads straight-forward to results of high accuracy

Optimal prediction for positive self-similar Markov processes

This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in Glover et al. (2013) under the assumption that X is a positive transient diffusion. We extend their result to the class of positive self-similar Markov processes by establishing a link to Baurdoux and van Schaik (2013), where the same question is studied for a Levy process drifting to minus infinity. The connection to Baurdoux and van Schaik (2013) relies on the so-called Lamperti transformation which links the class of positive self-similar Markov processes with that of Levy processes. Our approach will reveal that the results in Glover et al. (2013) for Bessel processes can also be seen as a consequence of self-similarity

Optimal double stopping of a Brownian bridge

We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type

Optimality of doubly reflected Lévy processes in singular control

We consider a class of two-sided singular control problems. A controller either increases or decreases a given spectrally negative Lévy process so as to minimize the total costs comprising of the running and controlling costs where the latter is proportional to the size of control. We provide a sufficient condition for the optimality of a double barrier strategy, and in particular show that it holds when the running cost function is convex. Using the fluctuation theory of doubly reflected Lévy processes, we express concisely the optimal strategy as well as the value function using the scale function. Numerical examples are provided to confirm the analytical results

On future drawdowns of Levy processes

For a given Levy process X = ( X t ) t 2 R + and for xed s 2 R + [f1g and t 2 R + we analyse the future drawdown extremes that are de ned as follows: The path-functionals D t;s and D t;s are of interest in various areas of application, including nancial mathematics and queueing theory. In the case that X has a strictly positive mean, we nd the exact asymptotic decay as x ! 1 of the tail probabilities P ( D t < x ) and P ( D t < x ) of D t = lim s !1 D t;s and D t = lim s !1 D t;s both when the jumps satisfy the Cram er assumption and in a heavy-tailed case. Furthermore, in the case that the jumps of the L evy process X are of single sign and X is not subordinator, we identify the one-dimensional distributions in terms of the scale function of X . By way of example, we derive explicit results for the Black- Scholes-Samuelson model