63 research outputs found
Optimal consumption and investment with bounded downside risk for power utility functions
We investigate optimal consumption and investment problems for a
Black-Scholes market under uniform restrictions on Value-at-Risk and Expected
Shortfall. We formulate various utility maximization problems, which can be
solved explicitly. We compare the optimal solutions in form of optimal value,
optimal control and optimal wealth to analogous problems under additional
uniform risk bounds. Our proofs are partly based on solutions to
Hamilton-Jacobi-Bellman equations, and we prove a corresponding verification
theorem. This work was supported by the European Science Foundation through the
AMaMeF programme.Comment: 36 page
A note on a result of Liptser-Shiryaev
Given two stochastic equations with different drift terms, under very weak
assumptions Liptser and Shiryaev provide the equivalence of the laws of the
solutions to these equations by means of Girsanov transform. Their assumptions
involve both the drift terms. We are interested in the same result but with the
main assumption involving only the difference of the drift terms. Applications
of our result will be presented in the finite as well as in the infinite
dimensional setting.Comment: 22 pages; revised and enlarged versio
Observability and nonlinear filtering
This paper develops a connection between the asymptotic stability of
nonlinear filters and a notion of observability. We consider a general class of
hidden Markov models in continuous time with compact signal state space, and
call such a model observable if no two initial measures of the signal process
give rise to the same law of the observation process. We demonstrate that
observability implies stability of the filter, i.e., the filtered estimates
become insensitive to the initial measure at large times. For the special case
where the signal is a finite-state Markov process and the observations are of
the white noise type, a complete (necessary and sufficient) characterization of
filter stability is obtained in terms of a slightly weaker detectability
condition. In addition to observability, the role of controllability in filter
stability is explored. Finally, the results are partially extended to
non-compact signal state spaces
Large closed queueing networks in semi-Markov environment and its application
The paper studies closed queueing networks containing a server station and
client stations. The server station is an infinite server queueing system,
and client stations are single-server queueing systems with autonomous service,
i.e. every client station serves customers (units) only at random instants
generated by a strictly stationary and ergodic sequence of random variables.
The total number of units in the network is . The expected times between
departures in client stations are . After a service completion
in the server station, a unit is transmitted to the th client station with
probability , and being processed in the th client
station, the unit returns to the server station. The network is assumed to be
in a semi-Markov environment. A semi-Markov environment is defined by a finite
or countable infinite Markov chain and by sequences of independent and
identically distributed random variables. Then the routing probabilities
and transmission rates (which are expressed via
parameters of the network) depend on a Markov state of the environment. The
paper studies the queue-length processes in client stations of this network and
is aimed to the analysis of performance measures associated with this network.
The questions risen in this paper have immediate relation to quality control of
complex telecommunication networks, and the obtained results are expected to
lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat
Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance
Published in Handbook of financial time series, 2008, https://doi.org/10.1007/978-3-540-71297-8_22</p
Maximum likelihood and Gaussian estimation of continuous time models in finance
Ministry of Education, Singapore under its Academic Research Funding Tier
Large Deviations For Unbounded Additive Functionals Of Markov Process With Discrete Time (non compact case)
. We combine the Donsker and Varadhan large deviation principle (l.d.p.) for the occupation measure of Markov process with certain results of Deuschel and Strook to obtain the l.d.p. for unbounded functionals. Our approach relies on the concept of exponential tightness and the Puhalskii theorem. Three illustrative examples are considered. Key words: Exponential tightness, Large deviations 1. Introduction and main result 1. Consider an ergodic Markov process ¸ = (¸ k ) k0 having R as its state space, 0 (dx) as the distribution of the initial point ¸ 0 , and = (dx) as the invariant measure. The transition probability ß(x; dy) is assumed to satisfy the Feller condition. From application point of view it is interesting to get the large deviations for functionals of the type ( 1 n P n\Gamma1 k=0 g(¸ k ); n 1) with a continuous unbounded function g = g(x). There exist different ways of solving this problem (see Gartner [8], Dueschel and Stroock [3], Veretennikov [13], Acosta [1], Elli..
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