18,259 research outputs found
Optimal dividend policies with random profitability
We study an optimal dividend problem under a bankruptcy constraint. Firms
face a trade-off between potential bankruptcy and extraction of profits. In
contrast to previous works, general cash flow drifts, including
Ornstein--Uhlenbeck and CIR processes, are considered. We provide rigorous
proofs of continuity of the value function, whence dynamic programming, as well
as comparison between the sub- and supersolutions of the
Hamilton--Jacobi--Bellman equation, and we provide an efficient and convergent
numerical scheme for finding the solution. The value function is given by a
nonlinear PDE with a gradient constraint from below in one dimension. We find
that the optimal strategy is both a barrier and a band strategy and that it
includes voluntary liquidation in parts of the state space. Finally, we present
and numerically study extensions of the model, including equity issuance and
credit lines
Subgame-Perfect Equilibria in Stochastic Timing Games
We introduce a notion of subgames for stochastic timing games and the related
notion of subgame-perfect equilibrium in possibly mixed strategies. While a
good notion of subgame-perfect equilibrium for continuous-time games is not
available in general, we argue that our model is the appropriate version for
timing games. We show that the notion coincides with the usual one for
discrete-time games. Many timing games in continuous time have only equilibria
in mixed strategies -- in particular preemption games, which often occur in the
strategic real option literature. We provide a sound foundation for some
workhorse equilibria of that literature, which has been lacking as we show. We
obtain a general constructive existence result for subgame-perfect equilibria
in preemption games and illustrate our findings by several explicit
applications.Comment: 27 pages, 1 figur
A class of recursive optimal stopping problems with applications to stock trading
In this paper we introduce and solve a class of optimal stopping problems of
recursive type. In particular, the stopping payoff depends directly on the
value function of the problem itself. In a multi-dimensional Markovian setting
we show that the problem is well posed, in the sense that the value is indeed
the unique solution to a fixed point problem in a suitable space of continuous
functions, and an optimal stopping time exists. We then apply our class of
problems to a model for stock trading in two different market venues and we
determine the optimal stopping rule in that case.Comment: 35 pages, 2 figures. In this version, we provide a general analysis
of a class of recursive optimal stopping problems with both finite-time and
infinite-time horizon. We also discuss other application
The least squares method for option pricing revisited
It is shown that the the popular least squares method of option pricing
converges even under very general assumptions. This substantially increases the
freedom of creating different implementations of the method, with varying
levels of computational complexity and flexible approach to regression. It is
also argued that in many practical applications even modest non-linear
extensions of standard regression may produce satisfactory results. This claim
is illustrated with examples
On strong solutions for positive definite jump-diffusions
We show the existence of unique global strong solutions of a class of
stochastic differential equations on the cone of symmetric positive definite
matrices. Our result includes affine diffusion processes and therefore extends
considerably the known statements concerning Wishart processes, which have
recently been extensively employed in financial mathematics. Moreover, we
consider stochastic differential equations where the diffusion coefficient is
given by the alpha-th positive semidefinite power of the process itself with
0.5<alpha<1 and obtain existence conditions for them. In the case of a
diffusion coefficient which is linear in the process we likewise get a positive
definite analogue of the univariate GARCH diffusions.Comment: version to appear in Stochastic Processes and Their Applications,
201
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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