Explicit correlations for the Hawkes processes

In this paper we fill a gap in the literature by providing exact and explicit expressions for the correlation of general Hawkes processes together with its intensity process. Our methodology relies on the Poisson imbedding representation and on recent findings on Malliavin calculus and pseudo-chaotic representation for counting processes

Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization.

In this paper we study BSDEs arising from a special class of backward stochastic partial differential equations (BSPDEs) that is intimately related to utility maximization problems with respect to arbitrary utility functions. After providing existence and uniqueness we discuss the numerical realizability. Then we study utility maximization problems on incomplete financial markets whose dynamics are governed by continuous semimartingales. Adapting standard methods that solve the utility maximization problem using BSDEs, we give solutions for the portfolio optimization problem which involve the delivery of a liability at maturity. We illustrate our study by numerical simulations for selected examples. As a byproduct we prove existence of a solution to a very particular quadratic growth BSDE with unbounded terminal condition. This complements results on this topic obtained in [6, 7, 8].numerical scheme; stochastic optimal control; utility optimization; quadratic growth; distortion transformation; logarithmic transformation; BSPDE; BSDE;

CRRA Utility Maximization under Dynamic Risk Constraints

The problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies, is the main focus of this paper. Several works in the literature, which deal either with optimal trading under static risk constraints or with VaR{based dynamic risk constraints, are extended. The market model considered is continuous in time and incomplete, and the prices of financial assets are modeled by It^o processes. The dynamic risk constraints, which are time and state dependent, are generated by a general class of risk measures. Optimal trading strategies are characterized by a quadratic BSDE. Within the class of time consistent distortion risk measures, a three{fund separation result is established. Numerical results emphasize the effects of imposing risk constraints on trading

Modelling the distribution of rare and data-poor diadromous fish at sea for protected area management

Anthropogenic pressures have resulted in declines in diadromous fish. Many diadromous fish which were commercially important are now threatened and protected. Little is known about their marine life history phases, and no observation-based Species Distribution Model exists for this group of species at sea. Yet, fisheries dependent and independent data could provide new insights into the distribution of diadromous fish at sea.We collated a database of 168 904 hauls from fisheries observer bycatch data and scientific fisheries surveys, from eastern Atlantic and Mediterranean waters. The distribution of eleven rare and data-poor diadromous fish (shads, lampreys, salmonids, the European eel, the thinlip mullet, smelt and the European flounder) were modelled. A Bayesian site occupancy model, that incorporates imperfect detection to account for repeat de-tections and non-detections, the non-random nature of fishing gear type and spatial autocorrelation was used. From the model outputs, we explored bycatch risk and the role of MPAs, required under the Marine Strategy Framework Directive and Habitat Directive and assessed.Diadromous fish were observed within relatively shallow coastal areas. Species specific gear bycatch trends were observed. Core distribution areas corresponded to their known water basin presence, indicating connec-tivity with their freshwater habitats. Numerous Habitat Directive Marine Protected Areas were found to be of relevance.Given the coastal distribution of these species, they are exposed to higher anthropogenic pressures from both terrestrial and marine environments. Risk of bycatch at sea for most species appears to be low. Nonetheless, for threatened individuals, even a small amount of bycatch may impact their populations, especially since mis-reporting is likely to be high. Differences in catchability between gears highlight potential benefits of limiting access of certain gears within protected areas to reduce bycatch