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Browsing Statistics by Author "Elliott, R."

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    A Bayesian approach for optimal reinsurance and investment in a diffusion model
    (Kluwer Academic Publ, 2012) Zhang, X.; Elliott, R.; Siu, T.
    A Bayesian adaptive control approach to the combined optimal investment/reinsurance problem of an insurance company is studied. The insurance company invests in a money market and a capital market index with an unknown appreciation rate, or “drift”. Using a Bayesian approach, the unknown drift is described by an unobservable random variable with a known (prior) probability distribution. We assume that the risk process of the company is governed by a diffusion approximation to the compound Poisson risk process. The company also purchases reinsurance. The combined optimal investment/reinsurance problem is formulated as a stochastic optimal control problem with partial observations. We employ filtering theory to transform the problem into one with complete observations. The control problem is then solved by the dynamic programming Hamilton–Jacobi–Bellman (HJB) approach. Semi-analytical solutions are obtained for the exponential utility case.
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    Existence, uniqueness and comparisons for BSDEs in general spaces
    (Inst Mathematical Statistics, 2012) Cohen, S.; Elliott, R.
    We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time and allow discrete processes to be embedded with continuous ones.We also present conditions for a comparison theorem and hence construct time consistent nonlinear expectations in these general spaces.