Robust estimation for ARMA models

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorably with respect to standard M-estimates and to estimates based on a diagnostic procedure.Comment: Published in at http://dx.doi.org/10.1214/07-AOS570 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal investment policy and dividend payment strategy in an insurance company

We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cram\'{e}r--Lundberg process. The firm has the option of investing part of the surplus in a Black--Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the smallest viscosity solution of the associated second-order integro-differential Hamilton--Jacobi--Bellman equation. We study the regularity of the optimal value function. We show that the optimal dividend payment strategy has a band structure. We find a method to construct a candidate solution and obtain a verification result to check optimality. Finally, we give an example where the optimal dividend strategy is not barrier and the optimal value function is not twice continuously differentiable.Comment: Published in at http://dx.doi.org/10.1214/09-AAP643 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Identifying plant functional traits to assist ecological intervention in a drying landscape

Mediterranean-type ecosystems (MTEs) are among the most vulnerable to land use and climate change and many attempts are in place to restore these ecosystems. Therefore, it is necessary to assess differences in plants’ ability to withstand water-stress, including biotic interactions. Such knowledge helps us understand community assembly, which is crucial for ecological intervention. This study involved: (1) reviewing the literature on traits that can differentiate functional types; (2) adapting the methodology to measure leaf water potential at turgor loss point (πtlp) for small-leaved species; (3) using these traits to quickly identify water-use strategies of adult plants from Southwest Australia; (4) identifying the water-use strategies that juveniles have to survive first summer drought; and (5) determining whether there is facilitation between a deep-rooted species and seedlings through hydraulic redistribution. The selection of functional response traits was based on their association with water-stress, with effect traits, and on methodologies that are easy, inexpensive and applicable for Mediterranean species. Relevant traits were identified from the literature, including: leaf carbon isotope composition, leaf nitrogen and phosphorus contents, leaf mass per area, πtlp, and xylem vessel morphology. Measurements of πtlp through osmometry of extracted sap and through Pressure-volume curves were compared. Selected traits were then measured for 15 species from different eco-hydrological habitats. Drought resistance of juveniles was assessed by measuring water relations, rooting depth/pattern and carbon reserves use of species from different eco-hydrological habitats. Lastly, seedlings were grown isolated or near donor plants. Water status and growth were measured, and stable isotopes were used to investigate water pathways within and between plants. A strong correlation between the methodologies for measuring πtlp was found. With analysis of these traits, it was possible to cluster adult species, from the Swan Coastal plain, into five functional groups that corresponded to their rooting depths. During drought, Banksia seedlings reduced stomatal conductance and appeared to use carbon reserves, whereas Gompholobium tomentosum seedlings tolerated higher water deficits, despite reduced stomatal conductance. Lastly, although seedlings were able to absorb hydraulically redistributed water, they grew, transpired and survived more when isolated from the deep-rooted plant. In the literature review, theoretical analyses on functional traits and speculations on functional groups were made through a conceptual diagram. The osmometry technique is a suitable replacement for Pressure-volume curves since its estimations of πtlp were accurate in small and large-leaved species. The functional traits approach can be transferable to other MTEs for application by restoration practitioners, as the traits selected were effective in determining functional groups, and were relatively easy and cost effective. The seedlings’ responses to summer drought were consistent with their habitats and root-depth, which is an important factor for niche differentiating and community assembly. Competition between seedlings and deep-rooted plants supported the updated stress-gradient hypothesis. In conclusion, analyses of water-use strategies of Mediterranean species during summer allow predictions of differences in drought resistance. When this functional approach is applied for ecological intervention, restoration practitioners can select species with a better match to future environmental conditions of MTEs, particularly in large species sets

Optimal dividend strategies for two collaborating insurance companies

We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We solve the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending results of univariate optimal control theory. In the case that the dividends paid by the two companies are equally weighted, the value function of this problem compares favorably with the one of merging the two companies completely. We identify this optimal value function as the smallest viscosity supersolution of the respective Hamilton-Jacobi-Bellman equation and provide an iterative approach to approximate it numerically. Curve strategies are identified as the natural analogue of barrier strategies in this two-dimensional context. A numerical example is given for which such a curve strategy is indeed optimal among all admissible dividend strategies, and for which this collaboration mechanism also outperforms the suitably weighted optimal dividend strategies of the two stand-alone companies

Optimal dividend strategies for a catastrophe insurer

In this paper we study the problem of optimally paying out dividends from an insurance portfolio, when the criterion is to maximize the expected discounted dividends over the lifetime of the company and the portfolio contains claims due to natural catastrophes, modelled by a shot-noise Cox claim number process. The optimal value function of the resulting two-dimensional stochastic control problem is shown to be the smallest viscosity supersolution of a corresponding Hamilton-Jacobi-Bellman equation, and we prove that it can be uniformly approximated through a discretization of the space of the free surplus of the portfolio and the current claim intensity level. We implement the resulting numerical scheme to identify optimal dividend strategies for such a natural catastrophe insurer, and it is shown that the nature of the barrier and band strategies known from the classical models with constant Poisson claim intensity carry over in a certain way to this more general situation, leading to action and non-action regions for the dividend payments as a function of the current surplus and intensity level. We also discuss some interpretations in terms of upward potential for shareholders when including a catastrophe sector in the portfolio.Este artículo se encuentra originalmente publicado en Frontiers of Mathematical Finance (e- ISSN:2769-6715

Optimal strategies in a production-inventory control model

We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory to switch-off when the inventory process reaches the storage maximum capacity. We consider holding, production, shortage penalty and switching costs. This model was introduced by Doshi, Van Der Duyn Schouten and Talman in 1978. Our aim is to minimize the expected discounted cumulative costs up to infinity over all admissible switching strategies. We show that the optimal cost functions for the different production rates satisfy the corresponding Hamilton-Jacobi-Bellman system of equations in a viscosity sense and prove a verification theorem. The way in which the optimal cost functions solve the different variational inequalities gives the switching regions of the optimal strategy, hence it is stationary in the sense that depends only on the current production rate and inventory level. We define the notion of finite band strategies and derive, using scale functions, the formulas for the different costs of the band strategies with one or two bands. We also show that there are examples where the switching strategy presented by Doshi et al. is not the optimal strategy.Comment: 31 pages, 15 figure

Optimal dividend strategies for a catastrophe insurer

In this paper we study the problem of optimally paying out dividends from an insurance portfolio, when the criterion is to maximize the expected discounted dividends over the lifetime of the company and the portfolio contains claims due to natural catastrophes, modelled by a shot-noise Cox claim number process. The optimal value function of the resulting two-dimensional stochastic control problem is shown to be the smallest viscosity supersolution of a corresponding Hamilton-Jacobi-Bellman equation, and we prove that it can be uniformly approximated through a discretization of the space of the free surplus of the portfolio and the current claim intensity level. We implement the resulting numerical scheme to identify optimal dividend strategies for such a natural catastrophe insurer, and it is shown that the nature of the barrier and band strategies known from the classical models with constant Poisson claim intensity carry over in a certain way to this more general situation, leading to action and non-action regions for the dividend payments as a function of the current surplus and intensity level. We also discuss some interpretations in terms of upward potential for shareholders when including a catastrophe sector in the portfolio