Solutions of Backward Stochastic Differential Equations on Markov Chains

We consider backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We show that appropriate solutions exist for arbitrary terminal conditions, and are unique up to sets of measure zero. We do not require the generating functions to be monotonic, instead using only an appropriate Lipschitz continuity condition.Comment: To appear in Communications on Stochastic Analysis, August 200

Filters and smoothers for self-exciting Markov modulated counting processes

We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this filter both with simulated data, and by analysing the `flash crash' of 6th May 2010 in this framework

Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions

Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expectations in the spirit of [Dynamically consistent nonlinear evaluations and expectations (2005) Shandong Univ.]. We prove basic properties of these expectations and show their applications to dynamic risk measures on such spaces. In particular, we prove comparison theorems for scalar and vector valued solutions to BSDEs, and discuss arbitrage and risk measures in the scalar case.Comment: Published in at http://dx.doi.org/10.1214/09-AAP619 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parasitism of Early Instar Jack Pine Budworm (Lepidoptera: Tortricidae) by Apanteles Spp. (Hymenoptera: Braconidae) and Glypta Fumiferanae (Hymenoptera: Ichneumonidae)

Glypta fumiferanae and two species of Apanteles parasitized 1st-4th instar jack pine bud worm (Choristoneura pinus). Apparent parasitism of budworm in four Michigan populations ranged from 10.6 to 30.9% for A. fumiferanae, 4.3-16.4% for A. morrisi, and 2.1-9.1 % for G.fumiferanae. A. morrisi probably parasitized 3rd-4th instar jack pine bud worm. Based on the results obtained, it is suggested that sampling overwintering budworm larvae is appropriate for estimating apparent parasitism by A. fumiferanae and G. fumiferanae. Sampling budworm larvae at ca. 500 degree-days (base 8.9°C) is appropriate for estimating apparent parasitism by A. morrisi

Aphidophagous Coccinellids in Alfalfa, Small Grains, and Maize in Eastern South Dakota

In a 13-year study of aphidophagous coccinellids associated with alfalfa (Medicago sativa), maize (Zea mays), and small grain crops in eastern South Dakota, the following species were consistently associated with the crops: Hippodamia convergens, H. tredecimpunctata tibialis, H. parenthesis, Coleomegilla maculata lengi, Coccinella transversoguttata richardsoni, Cycloneda munda, and Adalia bipunctata. All species except A. bipunctata were associated with each of the three crops, while A. bipunctata occurred only in maize. Relative abundances of each species varied among crops and among years. Although only seven species were associated with the crops, additional species were captured on sticky traps stationed adjacent to sampled fields. The species diversity of immature coccinellids did not differ among crops but did differ among years. The diversity of adults differed among crops and years. The site from which samples were taken had no influence on the diversity of immatures or adults. Species relative abundances in alfalfa and small grains were more similar to each other than they were to relative abundances in maize