Fin & math doc seminar

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8 October 2013
11:15-12:00

Dr. Philipp Harms

Event Details

Title	Two-Armed Restless Bandits with Imperfect Information
Speaker, Affiliation	Dr. Philipp Harms,
Date, Time	8 October 2013, 11:15-12:00
Location	HG G 19.2
Abstract	We present a two-armed bandit model of decision making under uncertainty where the expected return to investing in the “risky arm” increases when choosing that arm and decreases when choosing the “safe” arm. These dynamics are natural in applications such as human capital development, job search, and occupational choice. Using new insights from stochastic control, along with a monotonicity condition on the payoff dynamics, we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with Gittins’ index. Our result implies the indexability of a new class of “restless” bandit models. Preprint: http://www.nber.org/papers/w19043

Two-Armed Restless Bandits with Imperfect Informationread_more

19 November 2013
11:15-12:00

Nicoletta Gabrielli

Event Details

Title	Regularity results for degenerate Kolmogorov equations of affine type
Speaker, Affiliation	Nicoletta Gabrielli,
Date, Time	19 November 2013, 11:15-12:00
Location	HG G 19.2
Abstract	A common problem faced in mathematical finance is the efficient computation of expectations of functionals arising from the pricing of derivative contracts. A possible way to look at this quantity is by means of the Kolmogorov equation corresponding to the pricing problem. One of the main features of affine-type operators is its degeneracy and the lack of Lipschitz regularity. In this talk we analyze a new representation of affine processes as path-space valued Levy processes. This new representation not only leads to a new perspective on numerics of affine processes but is also essential to prove regularity of degenerate Kolmogorov equations with unbounded initial condition.

Regularity results for degenerate Kolmogorov equations of affine typeread_more

10 December 2013
11:15-12:00

Nikola Vasiljevic

Event Details

Title	American Options in a Jump-Diffusion Model: Randomization and Disentanglement
Speaker, Affiliation	Nikola Vasiljevic,
Date, Time	10 December 2013, 11:15-12:00
Location	HG G 19.2
Abstract	We analyze American options in a hyper-exponential jump-diffusion model. The model allows for an approximation of any Lévy process, and is general enough to capture salient features of underlying asset and related option prices. Our contribution is threefold. First, by following the Gaver-Stehfest maturity randomization approach, we solve the partial integro-differential equation and apply an efficient numerical procedure to obtain a tight lower bound for the option price. Secondly, we analyze the randomization technique for American options in a jump-diffusion setting and compare it with alternative methods in terms of speed and accuracy. Finally, embedding the existing results regarding the Laplace transform of the first-hitting time in the randomization method allows us to disentangle the early exercise contributions of jump and diffusion components of the underlying process. Hence, we can quantify the impact of the possibility of an overshoot. The main advantages of the Gaver-Stehfest randomization approach are analytical tractability, speed, and new economic insight for American option pricing in jump-diffusion framework.

American Options in a Jump-Diffusion Model: Randomization and Disentanglementread_more

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Organizers: Martin Herdegen

Archive: SS 15 AS 14 SS 14 AS 13 SS 13 AS 12