We consider the complexity of the Hamilton cycle decision problem when restricted to k-uniform hypergraphs H of high minimum codegree δ(H). We show that for tight Hamilton cycles this problem is NP-hard even when restricted to k-uniform hypergraphsH with δ(H) ≥ n2−C, where n is the order of H and C is a constant which depends only on k. This answers a question raised by Karpiński, Ruciński and ...

The illiquid market model HJB equations and characterization of the solution Power utility functions and numerical results

In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for evolutionary HJB equation with nonlinear source terms with the mixed boundary conditions and a general elliptic operator. Moreover, an asymptotic behavior in uniform norm is established.

We study an optimal investment and risk control problem for an insurer under stochastic factor. The insurer allocates his wealth across a riskless bond and a risky asset whose drift and volatility depend on a factor process. The risk process is modeled by a jump-diffusion with state-dependent jump measure. By maximizing the expected power utility of the terminal wealth, we characterize the opti...

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the erg...

A π,z J(z) = lim t>0,t→0 e −αt E z,π [J(z(t))] − J(z) t Lemma 1. Let J ∈ J satisfy J(0, a, b) = 0. Let τ = inf{t : J(z t) = 0}. E τ 0 e −αt e −π(z)/r a b π(z) + A π,z J(z) dt = J π (z 0) − J(z 0) Proof: Define H π J(z) = e −π(z)/r a b π(z) + A π,z J(z) Lemma 6 later verifies that this definition is in agreement with our previous definition (in [2]) provided J ∈ J. Let τ be a stopping time of th...

It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge disjoint Hamilton cycles, [4], [13], [9]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ≥ 2, if random edges of Kn are presented one by one then w.h.p. it is possible to color the edges online with σ color...

In this paper we discuss the applications of the Hamilton-Pontryagin variational principle for designing time-adaptive variational integrators. First, we review the multisymplectic formalism of field theories. Next, we review the Hamilton-Pontryagin principle and show how it can be used to handle time reparametrizations in a very natural way. Finally, we derive a time-adaptive variational integ...

In the late 70s, it was shown by Komlós and Szemerédi ([7]) that for p = lnn+ln lnn+c n , the limit probability for G(n, p) to contain a Hamilton cycle equals the limit probability for G(n, p) to have minimum degree at least 2. A few years later, Ajtai, Komlós and Szemerédi ([1]) have shown a hitting time version of this in the G(n,m) model. Say a graph G has property H if it contains bδ(G)/2c ...

In this article current directions in solving Lovász’s problem about the existence of Hamilton cycles and paths in connected vertex-transitive graphs are given. © 2009 Elsevier B.V. All rights reserved. 1. Historical motivation In 1969, Lovász [59] asked whether every finite connected vertex-transitive graph has a Hamilton path, that is, a simple path going through all vertices, thus tying toge...