No abstract

An improved fractal-based detector using the normalised Hurst exponent is proposed to detect floating small targets in sea clutter. Analysis of the IPIX radar datasets shows that the Hurst exponent of sea clutter varies with sea state and the viewing geometry of the radar. Referring to the exploitation of the reference range cells in adaptive detection, the mean and variance of the Hurst exponent of sea clutter are first computed from clutter-only time series at the reference range cells around the cell under test (CUT). Then the Hurst exponent at the CUT is normalised by the estimated mean and variance to attain the normalised Hurst exponent. The experimental results of the IPIX radar datasets show that the fractal-based detector using the normalised Hurst exponent achieves better detection performance.

A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least C 2 , we show that bifurcations of a coindex-1 heterodimensional cycle within a generic 2-parameter family always create robust heterodimensional dynamics, i.e., chain-transitive sets which contain coexisting orbits with different numbers of positive Lyapunov exponents and persist for an open set of parameter values. In particular, we solve the so-called C r -stabilization problem for the coindex-1 heterodimensional cycles in any regularity class r = 2, . . . , ∞, ω. The results are based on the observation that arithmetic properties of moduli of topological conjugacy of systems with heterodimensional cycles determine the emergence of Bonatti-Díaz blenders.

No abstract

In this paper, we study an insurer's reinsurance-investment problem under a mean-variance criterion. We show that excess-loss is the unique equilibrium reinsurance strategy under a spectrally negative Lévy insurance model when the reinsurance premium is computed according to the expected value premium principle. Furthermore, we obtain the explicit equilibrium reinsurance-investment strategy by solving the extended Hamilton-Jacobi-Bellman equation.JEL Codes: C730, G220.1 in which γ is the absolute risk aversion of the utility maximizer. Note that maximizing (1.1) is precisely the mean-variance criterion. Also, under fairly general conditions, optimal insurance is deductible insurance for a risk-averse utility maximizer (see, for example, Arrow [1], van Heervarden [25], and Moore and Young [20]). Thus, when maximizing (1.1) (or solving a related game) with Y equal to terminal wealth of an insurance company, we expect that optimal (or equilibrium) reinsurance will be deductible, or excess-loss, reinsurance, which we prove below in Theorem 3.2. Furthermore, because the risk aversion γ is constant, the deductible is independent of the surplus of the insurer. Under the mean-variance criterion, the reinsurance-investment problem is time-inconsistent in the sense that Bellman's optimality principle fails. To tackle the time inconsistency, we formulate the problem as a non-cooperative game and solve for a subgame perfect Nash equilibrium. Specifically, at every time point, the player solves for an equilibrium strategy by treating the problem as a game against all future versions of himself. An equilibrium strategy is, thus, time-consistent. One can trace this approach to Strotz [24], and it has recently been further developed by Björk and Murgoci [7] for a general class of objective functions in a Markovian framework. Due to the importance of time consistency for a rational insurer, the approach has already been applied by many authors to solve for equilibrium strategies in the literature of reinsurance-investment problems (see, for example, Zeng et al. [28] and Lin and Qian [17]).Two types of reinsurance policies are most commonly studied in the literature on equilibrium reinsurance and investment under a mean-variance criterion: (1) proportional (quota-share) reinsurance (see, for example, Zeng and Li [27], Shen and Zeng [23], and the two references given at the end of the previous paragraph) and (2) excess-loss reinsurance (see, for example, Li et al. [14]). Given the rich literature, one question naturally arises which has not received much attention: Which reinsurance policy yields an equilibrium for an insurer under a mean-variance criterion among all reasonable reinsurance policies? We show that buying excess-loss reinsurance is the unique equilibrium strategy under this criterion.We model the insurer's basic surplus process, that is, the surplus process without any reinsuranceinvestment strategy, by a spectrally negative Lévy process. The model is widely employed in the context of risk theory in the actuarial lite...