scholarly journals Financial Applications of Bivariate Markov Processes

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Sergio Ortobelli Lozza ◽  
Enrico Angelelli ◽  
Annamaria Bianchi
Keyword(s):  
Risk Management ◽  
Markov Chain ◽  
Markov Process ◽  
Option Pricing ◽  
Markov Processes ◽  
Joint Distribution ◽  
Large Scale ◽  
Portfolio Theory ◽  
Asian Options ◽  
Financial Applications

This paper describes a methodology to approximate a bivariate Markov process by means of a proper Markov chain and presents possible financial applications in portfolio theory, option pricing and risk management. In particular, we first show how to model the joint distribution between market stochastic bounds and future wealth and propose an application to large-scale portfolio problems. Secondly, we examine an application to VaR estimation. Finally, we propose a methodology to price Asian options using a bivariate Markov process.

A note on functions of Markov processes with an application to a sequence of χ2 statistics

1973 ◽  
Vol 10 (4) ◽  
pp. 895-900
Author(s):  
Murray A. Cameron
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Joint Distribution ◽  
Sufficient Condition ◽  
Simple Derivation ◽  
Reverse Process

A sufficient condition for a function of a Markov process to be Markovian is obtained by considering a reverse process of the original Markov process. An application of this result provides a simple derivation of the joint distribution of a sequence of Pearson χ2 statistics previously obtained by Zaharov, Sarmanov and Sevast'ianov (1969).

On occupation times for quasi-Markov processes

1981 ◽  
Vol 18 (01) ◽  
pp. 297-301 ◽  
Author(s):  
Lennart Bondesson
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Joint Distribution ◽  
Stieltjes Transform ◽  
Occupation Times ◽  
The Laplace Transform ◽  
The Times

In this note the joint distribution for the times in an interval [0, t] spent in the states 1, 2, ···, N in a standard quasi-Markov process of order N is considered. An expression for the Laplace transform with respect to t of the Laplace–Stieltjes transform of this joint distribution is derived.

Resolvent operators of Markov processes and their applications in the control of a finite dam

1989 ◽  
Vol 26 (2) ◽  
pp. 314-324 ◽  
Author(s):  
F. A. Attia
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Wiener Process ◽  
Markov Processes ◽  
Resolvent Operators ◽  
Input Process ◽  
Long Run ◽  
Negative Drift ◽  
Finite Dam ◽  
Irreducible Markov Chain

The resolvent operators of the following two processes are obtained: (a) the bivariate Markov process W = (X, Y), where Y(t) is an irreducible Markov chain and X(t) is its integral, and (b) the geometric Wiener process G(t) = exp{B(t} where B(t) is a Wiener process with non-negative drift μ and variance parameter σ2. These results are then used via a limiting procedure to determine the long-run average cost per unit time of operating a finite dam where the input process is either X(t) or G(t). The system is controlled by a policy (Attia [1], Lam [6]).

ACCELERATING MONTE CARLO MARKOV PROCESSES

COSMOS ◽  
2005 ◽  
Vol 01 (01) ◽  
pp. 87-94 ◽  
Author(s):  
CHII-RUEY HWANG
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Process ◽  
Markov Processes ◽  
Transition Matrix ◽  
Asymptotic Variance ◽  
Suitable Condition ◽  
Transition Matrices ◽  
Finite Set ◽  
The Continuum

Let π be a probability density proportional to exp - U(x) in S. A convergent Markov process to π(x) may be regarded as a "conceptual" algorithm. Assume that S is a finite set. Let X0,X1,…,Xn,… be a Markov chain with transition matrix P and invariant probability π. Under suitable condition on P, it is known that [Formula: see text] converges to π(f) and the corresponding asymptotic variance v(f, P) depends only on f and P. It is natural to consider criteria vw(P) and va(P), defined respectively by maximizing and averaging v(f, P) over f. Two families of transition matrices are considered. There are four problems to be investigated. Some results and conjectures are given. As for the continuum case, to accelerate the convergence a family of diffusions with drift ∇U(x) + C(x) with div(C(x)exp - U(x)) = 0 is considered.

On occupation times for quasi-Markov processes

1981 ◽  
Vol 18 (1) ◽  
pp. 297-301 ◽  
Author(s):  
Lennart Bondesson
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Joint Distribution ◽  
Stieltjes Transform ◽  
Occupation Times ◽  
The Laplace Transform ◽  
The Times

In this note the joint distribution for the times in an interval [0, t] spent in the states 1, 2, ···, N in a standard quasi-Markov process of order N is considered. An expression for the Laplace transform with respect to t of the Laplace–Stieltjes transform of this joint distribution is derived.

On a fundamental identity in the theory of semi-Markov processes

1972 ◽  
Vol 4 (02) ◽  
pp. 258-270 ◽  
Author(s):  
E. Arjas
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Markov Processes ◽  
Partial Sums ◽  
Discrete State ◽  
Fundamental Identity ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Wald's Identity ◽  
Discrete State Space

A fundamental identity, due to Miller (1961a), (1962a, b) and Kemperman (1961), is generalized to semi-Markov processes. Thus the identity applies to processes defined on a Markov chain with discrete state space and random walks with Markov dependent steps (Section 2). Wald's identity is discussed briefly in Section 3. Section 4 is a study of the maxima of partial sums, and Section 5 of maxima in a semi-Markov process.

Resolvent operators of Markov processes and their applications in the control of a finite dam

1989 ◽  
Vol 26 (02) ◽  
pp. 314-324 ◽  
Author(s):  
F. A. Attia
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Wiener Process ◽  
Markov Processes ◽  
Resolvent Operators ◽  
Input Process ◽  
Long Run ◽  
Negative Drift ◽  
Finite Dam ◽  
Irreducible Markov Chain

The resolvent operators of the following two processes are obtained: (a) the bivariate Markov process W = (X, Y), where Y(t) is an irreducible Markov chain and X(t) is its integral, and (b) the geometric Wiener process G(t) = exp{B(t} where B(t) is a Wiener process with non-negative drift μ and variance parameter σ2. These results are then used via a limiting procedure to determine the long-run average cost per unit time of operating a finite dam where the input process is either X(t) or G(t). The system is controlled by a policy (Attia [1], Lam [6]).

A note on functions of Markov processes with an application to a sequence of χ2 statistics

1973 ◽  
Vol 10 (04) ◽  
pp. 895-900
Author(s):  
Murray A. Cameron
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Joint Distribution ◽  
Sufficient Condition ◽  
Simple Derivation ◽  
Reverse Process

A sufficient condition for a function of a Markov process to be Markovian is obtained by considering a reverse process of the original Markov process. An application of this result provides a simple derivation of the joint distribution of a sequence of Pearson χ 2 statistics previously obtained by Zaharov, Sarmanov and Sevast'ianov (1969).

On a fundamental identity in the theory of semi-Markov processes

1972 ◽  
Vol 4 (2) ◽  
pp. 258-270 ◽  
Author(s):  
E. Arjas
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Markov Processes ◽  
Partial Sums ◽  
Discrete State ◽  
Fundamental Identity ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Wald's Identity ◽  
Discrete State Space

A fundamental identity, due to Miller (1961a), (1962a, b) and Kemperman (1961), is generalized to semi-Markov processes. Thus the identity applies to processes defined on a Markov chain with discrete state space and random walks with Markov dependent steps (Section 2). Wald's identity is discussed briefly in Section 3. Section 4 is a study of the maxima of partial sums, and Section 5 of maxima in a semi-Markov process.

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