In this paper, we derive an explicit solution to the utility maximization problem of individual with mortality risk and subsistence consumption constraint. We adopt exponential for individual’s martingale duality method is employed. From solution, exhibit how intensity constraint affect, separately together, portfolio, life insurance purchase.

ABSTRACT. In a previous work by the first author with J. Turi [2], a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major advantage of the stochastic variational inequality is to overcome the need to describe the trajectory by phases (elastic or plastic). This is useful, since the sequence of phases cannot be characterized easily. In pa...

For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its generating function, when assuming that the distribution of the jump in the direction making the exit possible has a Laplace transform which is a rational function. The expected exit time is also de...

We consider local martingales of exponential form M = eX or E (X) where X denotes one component of a multivariate affine process. We give a weak sufficient criterion for M to be a true martingale. As a first application, we derive a simple sufficient condition for absolute continuity of the laws of two given affine processes. As a second application, we study whether the exponential moments of ...

We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro-differential equations. Conditions are provided under which preservation of convexity holds, i.e. under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the u...

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, diffusion models can be obtained from these equations as approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using ...

We provide an analogue of Gundy’s decomposition for L1-bounded non-commutative martingales. An important difference from the classical case is that for any L1-bounded non-commutative martingale, the decomposition consists of four martingales. This is strongly related with the row/column nature of non-commutative Hardy spaces of martingales. As applications, we obtain simpler proofs of the weak ...

In the present work, we consider spectrally positive Lévy processes (Xt, t ≥ 0) not drifting to +∞ and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with X) before hitting 0. This way we obtain a new conditioning of Lévy processes to stay positive. The (honest) law Px of this conditioned process is defined as ...

Given (Mt)t∈R+ and (M ∗ t )t∈R+ respectively a forward and a backward martingale with jumps and continuous parts, we prove that E[φ(Mt + M ∗ t )] is nonincreasing in t when φ is a convex function, provided the local characteristics of (Mt)t∈R+ and (M ∗ t )t∈R+ satisfy some comparison inequalities. We deduce convex concentration inequalities and deviation bounds for random variables admitting a ...