Optimal stopping and the American put under incomplete information
نویسندگان
چکیده
Optimal stopping is a sub-field of probability theory that is present within mathematical finance, mathematical statistics, stochastic calculus and other disciplines. In mathematical finance, one well known problem is the pricing of an American put option. In this thesis we first give a brief review of some general optimal stopping theory, its connection to free-boundary problems and we then extend the problem of pricing the American put option to the case with incomplete information about the drift of the underlying stock.
منابع مشابه
Valuation for an American Continuous-Installment Put Option on Bond under Vasicek Interest Rate Model
The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim’s equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optim...
متن کاملOptimal stopping times with different information levels and with time uncertainty
Optimization/control problems with change of filtartions have been studied in various context of mathematical finance. This paper studies optimal stopping problems for general diffusion processes with an uncertain time horizon and under different filtrations. Corresponding value functions are first compared and related explicitly to their counterparts without the time uncertainty. To further an...
متن کاملClosed-Form Solutions for Perpetual American Put Options with Regime Switching
This paper studies an optimal stopping time problem for pricing perpetual American put options in a regime switching model. An explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the “modified smooth fit” technique. The solution is then compared with the numerical results obtained via a dynamic programming approach and also with a two-point bo...
متن کاملOptimal Stopping and Perpetual Options for L Evy Processes Optimal Stopping and Perpetual Options for L Evy Processes
Solution to the optimal stopping problem for a L evy process and reward functions (e x ?K) + and (K ?e x) + , discounted at a constant rate is given in terms of the distribution of the overall supremum and innmum of the process killed at this rate. Closed forms of this solutions are obtained under the condition of positive jumps mixed-exponentially distributed. Results are interpreted as admiss...
متن کاملOptimal Stopping, Free Boundary, and American Option in a Jump-Diffusion Model
This paper considers the American put option valuation in a jumpdiffusion model and relates this optimal-stopping problem to a parabolic integrodifferential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its...
متن کامل