We present some results on enlargement of filtration in discrete time. Many results known in continuous time extend immediately in a discrete time setting. Here, we provide direct proofs which are much more simpler. We study also arbitrages conditions in a financial setting and we present some specific cases, as immersion and pseudo-stopping times for which we obtain new results.

In this paper, we work on indifference valuation of variable annuities and give a computation method for indifference fees. We focus on the guaranteed minimum death benefits and the guaranteed minimum living benefits and allow the policyholder to make withdrawals. We assume that the fees are continuously payed and that the fee rate is fixed at the beginning of the contract. Following indifference pricing theory, we define indifference fee rate for the insurer as a solution of an equation involving two stochastic control problems. Relating these problems to backward stochastic differential equations with jumps, we provide a verification theorem and give the optimal strategies associated to our control problems. From these, we derive a computation method to get indifference fee rates. We conclude our work with numerical illustrations of indifference fees sensibilities with respect to parameters.

We present some results on enlargement of filtration in discrete time. Many results known in continuous time extend immediately in a discrete time setting. Here, we provide direct proofs which are much more simpler. We study also arbitrages conditions in a financial setting and we present some specific cases, as immersion and pseudo-stopping times for which we obtain new results.