Random jumps in the phase-OTDR response

2021 ◽  
Author(s):  
Alexey Alekseev ◽  
Boris Gorshkov ◽  
Vladimir Potapov ◽  
Denis Simikin ◽  
Mikhail Taranov
Keyword(s):  
Random Jumps

scholarly journals Option Pricing Driven by a Telegraph Process with Random Jumps

2012 ◽  
Vol 49 (3) ◽  
pp. 838-849 ◽  
Author(s):  
Oscar López ◽  
Nikita Ratanov
Keyword(s):  
Option Pricing ◽  
Financial Market ◽  
Option Prices ◽  
Martingale Measures ◽  
Market Models ◽  
Telegraph Process ◽  
Equivalent Martingale Measures ◽  
Hedging Strategies ◽  
Random Jumps ◽  
Equivalent Martingale

In this paper we propose a class of financial market models which are based on telegraph processes with alternating tendencies and jumps. It is assumed that the jumps have random sizes and that they occur when the tendencies are switching. These models are typically incomplete, but the set of equivalent martingale measures can be described in detail. We provide additional suggestions which permit arbitrage-free option prices as well as hedging strategies to be obtained.

scholarly journals ASYMPTOTIC BEHAVIOR OF THE PRINCIPAL EIGENVALUE FOR A CLASS OF NON-LOCAL ELLIPTIC OPERATORS RELATED TO BROWNIAN MOTION WITH SPATIALLY DEPENDENT RANDOM JUMPS

2011 ◽  
Vol 13 (06) ◽  
pp. 1077-1093
Author(s):  
NITAY ARCUSIN ◽  
ROSS G. PINSKY
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Principal Eigenvalue ◽  
Probability Measures ◽  
Rate Of Decay ◽  
Non Local ◽  
Random Jumps ◽  
Explicit Constant

Let D ⊂ Rd be a bounded domain and let [Formula: see text] denote the space of probability measures on D. Consider a Brownian motion in D which is killed at the boundary and which, while alive, jumps instantaneously according to a spatially dependent exponential clock with intensity γV to a new point, according to a distribution [Formula: see text]. From its new position after the jump, the process repeats the above behavior independently of what has transpired previously. The generator of this process is an extension of the operator -Lγ,μ, defined by [Formula: see text] with the Dirichlet boundary condition, where Cμ is the "μ-centering" operator defined by [Formula: see text] The principal eigenvalue, λ0(γ, μ), of Lγ, μ governs the exponential rate of decay of the probability of not exiting D for large time. We study the asymptotic behavior of λ0(γ, μ) as γ → ∞. In particular, if μ possesses a density in a neighborhood of the boundary, which we call μ, then [Formula: see text] If μ and all its derivatives up to order k - 1 vanish on the boundary, but the kth derivative does not vanish identically on the boundary, then λ0(γ, μ) behaves asymptotically like [Formula: see text], for an explicit constant ck.

scholarly journals Real option value and random jumps: application of a simulation model

2009 ◽  
Vol 41 (23) ◽  
pp. 2977-2989 ◽  
Author(s):  
Susana Alonso-Bonis ◽  
Valentín Azofra-Palenzuela ◽  
Gabriel de la Fuente-Herrero
Keyword(s):  
Simulation Model ◽  
Real Option ◽  
Option Value ◽  
Random Jumps ◽  
Real Option Value

Solving the Hamilton-Jacobi-Bellman equation of stochastic control by a semigroup perturbation method

1984 ◽  
Vol 16 (1) ◽  
pp. 16-16
Author(s):  
Domokos Vermes
Keyword(s):  
Bellman Equation ◽  
Value Function ◽  
Sufficient Optimality Condition ◽  
Hamilton Jacobi Bellman Equation ◽  
Deterministic Processes ◽  
Random Jumps ◽  
Hamilton Jacobi Bellman ◽  
Necessary And Sufficient ◽  
The Value Function ◽  
Deterministic Trajectories

We consider the optimal control of deterministic processes with countably many (non-accumulating) random iumps. A necessary and sufficient optimality condition can be given in the form of a Hamilton-jacobi-Bellman equation which is a functionaldifferential equation with boundary conditions in the case considered. Its solution, the value function, is continuously differentiable along the deterministic trajectories if. the random jumps only are controllable and it can be represented as a supremum of smooth subsolutions in the general case, i.e. when both the deterministic motion and the random jumps are controlled (cf. the survey by M. H. A. Davis (p.14)).

scholarly journals Counting processes with Bernštein intertimes and random jumps

2015 ◽  
Vol 52 (04) ◽  
pp. 1028-1044 ◽  
Author(s):  
Enzo Orsingher ◽  
Bruno Toaldo
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Negative Binomial ◽  
Counting Processes ◽  
Lévy Measure ◽  
Fractional Poisson Process ◽  
Independent Increments ◽  
Random Jumps ◽  
The Times ◽  
Passage Times

In this paper we consider point processes Nf (t), t > 0, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernštein functions f with Lévy measure v. We obtain the general expression of the probability generating functions Gf of Nf , the equations governing the state probabilities pk f of Nf , and their corresponding explicit forms. We also give the distribution of the first-passage times Tk f of Nf , and the related governing equation. We study in detail the cases of the fractional Poisson process, the relativistic Poisson process, and the gamma-Poisson process whose state probabilities have the form of a negative binomial. The distribution of the times of jumps with height lj () under the condition N(t) = k for all these special processes is investigated in detail.

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