Constructing Performance Sensitivities with Sample Paths in Continuous-time Markov Systems

2006 ◽  
Author(s):  
Fang Cao ◽  
Xi-Ren Cao
Keyword(s):  
Continuous Time ◽  
Markov Systems ◽  
Sample Paths

On certain aspects of non-homogeneous Markov systems in continuous time

1990 ◽  
Vol 27 (3) ◽  
pp. 530-544 ◽  
Author(s):  
Ioannis I. Gerontidis
Keyword(s):  
Continuous Time ◽  
Initial Distribution ◽  
Markov Systems ◽  
Numerical Examples ◽  
Stationary Structure ◽  
Periodic Environment ◽  
Time Formulation ◽  
Relative Structure ◽  
The Relationship ◽  
Theoretical Results

In the present paper we study three aspects in the theory of non-homogeneous Markov systems under the continuous-time formulation. Firstly, the relationship between stability and quasi-stationarity is investigated and conditions are provided for a quasi-stationary structure to be stable. Secondly, the concept of asymptotic attainability is studied and the possible regions of asymptotically attainable structures are determined. Finally, the cyclic case is considered, where it is shown that for a system in a periodic environment, the relative structure converges to a periodic vector, independently of the initial distribution. Two numerical examples illustrate the above theoretical results.

OPTIMAL GROWTH IN CONTINUOUS-TIME WITH CREDIT RISK

1999 ◽  
Vol 13 (2) ◽  
pp. 129-145 ◽  
Author(s):  
Sid Browne
Keyword(s):  
Brownian Motion ◽  
Credit Risk ◽  
Asset Allocation ◽  
Continuous Time ◽  
Average Rate ◽  
Optimal Growth ◽  
Expected Time ◽  
Sample Paths ◽  
Optimal Policies ◽  
Allocation Strategies

We consider asset allocation strategies for the case where an investor can allocate his wealth dynamically between a risky stock, whose price evolves according to a geometric Brownian motion, and a risky bond, whose price is subject to negative jumps due to its credit risk and therefore has discontinuous sample paths. We derive optimal policies for a number of objectives related to growth. In particular, we obtain the policy that minimizes the expected time to reach a given target value of wealth in an exact explicit form. We also show that this policy is exactly equivalent to the policy that is optimal for maximizing logarithmic utility of wealth and, hence, the expected average rate at which wealth grows, as well as to the policy that maximizes the actual asymptotic rate at which wealth grows. Our results generalize and unify results obtained previously for cases where the bond was risk-free in both continuous- and discrete-time.

Some stationary processes in discrete and continuous time

1998 ◽  
Vol 30 (04) ◽  
pp. 989-1007 ◽  
Author(s):  
O. E. Barndorff-Nielsen ◽  
J. L. Jensen ◽  
M. Sørensen
Keyword(s):  
Continuous Time ◽  
Stationary Processes ◽  
Marginal Distributions ◽  
Sample Paths ◽  
Stationary Stochastic Processes ◽  
The One ◽  
Log Linear ◽  
Infinite Sum ◽  
Discrete Time Models ◽  
Made In

A number of stationary stochastic processes are presented with properties pertinent to modelling time series from turbulence and finance. Specifically, the one-dimensional marginal distributions have log-linear tails and the autocorrelation may have two or more time scales. Discrete time models with a given marginal distribution are constructed as sums of independent autoregressions. A similar construction is made in continuous time by considering sums of Ornstein-Uhlenbeck-type processes. To prepare for this, a new property of self-decomposable distributions is presented. Also another, rather different, construction of stationary processes with generalized logistic marginal distributions as an infinite sum of Gaussian processes is proposed. In this way processes with continuous sample paths can be constructed. Multivariate versions of the various constructions are also given.

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