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Pekka Matomäki

Bio: Pekka Matomäki is an academic researcher from University of Turku. The author has contributed to research in topics: Optimal stopping & Optional stopping theorem. The author has an hindex of 5, co-authored 12 publications receiving 95 citations.

Papers
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Journal ArticleDOI
TL;DR: A two-sided singular control problem in a general linear diffusion setting is studied and a set of conditions under which an optimal control exists uniquely and is of singular control type is provided.
Abstract: We study a two-sided singular control problem in a general linear diffusion setting and provide a set of conditions under which an optimal control exists uniquely and is of singular control type. Moreover, under these conditions the associated value function can be written in a quasi-explicit form. Furthermore, we investigate comparative static properties of the solution with respect to the volatility and control parameters. Lastly we illustrate the results with two explicit examples.

34 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied a saddle point equilibrium in a Dynkin game with asymmetric information and proposed a set of conditions under which the saddle point equilibria can be solved.
Abstract: We study a Dynkin game with asymmetric information. The game has a random expiry time, which is exponentially distributed and independent of the underlying process. The players have asymmetric information on the expiry time, namely only one of the players is able to observe its occurrence. We propose a set of conditions under which we solve the saddle point equilibrium and study the implications of the information asymmetry. Results are illustrated with an explicit example.

29 citations

Journal ArticleDOI
TL;DR: In this article, a class of optimal stopping problems involving both the running maximum as well as the prevailing state of a linear diffusion is considered and a discretized approach resulting in a numerical algorithm for solving the considered class of stopping problems.
Abstract: We consider a class of optimal stopping problems involving both the running maximum as well as the prevailing state of a linear diffusion. Instead of tackling the problem directly via the standard free boundary approach, we take an alternative route and present a parameterized family of standard stopping problems of the underlying diffusion. We apply this family to delineate circumstances under which the original problem admits a unique, well-defined solution. We then develop a discretized approach resulting in a numerical algorithm for solving the considered class of stopping problems. We illustrate the use of the algorithm in both a geometric Brownian motion and a mean reverting diffusion setting.

9 citations

Dissertation
15 Nov 2013
TL;DR: In this article, the authors consider a situation where at any given time a company has three options: it can make an irreversible investmen t in order to obtain an improved technology resulting to a higher revenue flow, it can exit the market or it can postpone making the final decision.
Abstract: We study optimal timing in a combined investment and exit pro blem. We consider a situation where at any given time a company has t he following three options: It can make an irreversible investmen t in order to obtain an improved technology resulting to a higher revenue flow, it can exit the market or it can postpone making the final decision. W e prove the existence and uniqueness of an optimal strategy, which i s a two-sided threshold rule: exit below one threshold and invest above an other. We illustrate our results numerically with geometric Brownia motion. keywords: irreversible investment, exit, optimal stopping, linear d iffusion AMS Classification: 60G40, 62L15, 60J60

9 citations

Posted Content
TL;DR: The problem of representing the value of singular stochastic control problems of linear diffusions as expected suprema by setting the value accrued from following a standard reflection policy equal with the expected value of a unknown function at the running supremum of the underlying is considered.
Abstract: We consider the problem of representing the value of singular stochastic control problems of linear diffusions as expected suprema. Setting the value accrued from following a standard reflection policy equal with the expected value of a unknown function at the running supremum of the underlying is shown to result into a functional equation from which the unknown function can be explicitly derived. We also consider the stopping problem associated with the considered singular stochastic control problem and present a similar representation as an expected supremum in terms of characteristics of the control problem.

7 citations


Cited by
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Book ChapterDOI
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

2,446 citations

26 Nov 2005
TL;DR: In this article, the authors consider a general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities, and they show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process.
Abstract: We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process. Then we present stochastic numerical methods permitting the explicit computation of option prices and hedging strategies, and we illustrate our approach by specific examples.

137 citations

Posted Content
TL;DR: In this paper, the authors considered the problems of probability distributions and their characteristics for a Brownian motion, where the variables were considered for the variables and the characteristics of the distribution were considered.
Abstract: For a Brownian motion $B=(B_t)_{t\le 1}$ with $B_0=0$, {\bf E}$B_t=0$, {\bf E}$B_t^2=t$ problems of probability distributions and their characteristics are considered for the variables $$ \begin{array}{c} {\mathbb D} =\displaystyle\sup_{0\le t\le t'\le 1}(B_t-B_{t'}),\qquad {\mathbb D}_1=B_\sigma-\inf_{\sigma\le t'\le 1}B_{t'}, \\ {\mathbb D}_2=\displaystyle\sup_{0\le t\le\sigma'}B_{t}-B_{\sigma'}, \end{array} $$ where $\sigma$ and $\sigma'$ are times (non-Markov) of the absolute maximum and absolute minimum of the Brownian motion on $[0,1]$ (i.e., $B_\sigma=\sup_{0\le t\le 1}B_t$, $B_{\sigma'}=\inf_{0\le t'\le 1}B_{t'}$).

50 citations

Proceedings ArticleDOI
01 Dec 1984
TL;DR: In this paper, the authors consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients, and their objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process.
Abstract: We consider a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. Our objective is to minimize an integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of an appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be reduced to a simpler case of only one-sided control, i.e. a monotone follower. These results are applied to solving some examples by the so-called method of similarity solutions.

46 citations

Journal ArticleDOI
TL;DR: Among various results on game options the authors consider error estimates for their discrete approximations, swing game options, game options in markets with transaction costs and other questions.
Abstract: We start by briefly surveying a research on optimal stopping games since their introduction by Dynkin more than 40 years ago. Recent renewed interest to Dynkin’s games is due, in particular, to the study of Israeli (game) options introduced in 2000. We discuss the work on these options and related derivative securities for the last decade. Among various results on game options we consider error estimates for their discrete approximations, swing game options, game options in markets with transaction costs, and other questions.

45 citations