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Affine processes beyond stochastic continuity. (English) Zbl 1432.60073
Summary: In this paper, we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting, times of jumps can be both inaccessible and predictable. To this end, we develop a general theory of finite dimensional affine semimartingales under very weak assumptions. We show that the corresponding semimartingale characteristics have affine form and that the conditional characteristic function can be represented with solutions to measure differential equations of Riccati type. We prove existence of affine Markov processes and affine semimartingales under mild conditions and elaborate on examples and applications including affine processes in discrete time.

MSC:
60J25 Continuous-time Markov processes on general state spaces
91G20 Derivative securities (option pricing, hedging, etc.)
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