1,867 research outputs found
The strong predictable representation property in initially enlarged filtrations under the density hypothesis
We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional laws of L. Depending on the behavior of the density process at zero, different forms of martingale representation are established. The results are illustrated in the context of hedging contingent claims under insider information
Weak and strong no-arbitrage conditions for continuous financial markets
We propose a unified analysis of a whole spectrum of no-arbitrage conditions for finan- cial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage opportunity (NA) and No Free Lunch with Vanishing Risk (NFLVR). We provide a complete characterization of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results
No-arbitrage conditions and absolutely continuous changes of measure
We study the stability of several no-arbitrage conditions with respect to
absolutely continuous, but not necessarily equivalent, changes of measure. We
first consider models based on continuous semimartingales and show that
no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in
the context of general semimartingale models, we show that an absolutely
continuous change of measure does never introduce arbitrages of the first kind
as long as the change of measure density process can reach zero only
continuously.Comment: 14 pages. Arbitrage, Credit and Informational Risks (C. Hillairet, M.
Jeanblanc and Y. Jiao, eds.), Peking University Series in Mathematics, Vol.
6, World Scientific, 201
Arbitrage of the first kind and filtration enlargements in semimartingale financial models
In a general semimartingale financial model, we study the stability of the No
Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with
Bounded Risk) condition under initial and under progressive filtration
enlargements. In both cases, we provide a simple and general condition which is
sufficient to ensure this stability for any fixed semimartingale model.
Furthermore, we give a characterisation of the NA1 stability for all
semimartingale models.Comment: 27 page
Information, no-arbitrage and completeness for asset price models with a change point
We consider a general class of continuous asset price models where the drift
and the volatility functions, as well as the driving Brownian motions, change
at a random time . Under minimal assumptions on the random time and on
the driving Brownian motions, we study the behavior of the model in all the
filtrations which naturally arise in this setting, establishing martingale
representation results and characterizing the validity of the NA1 and NFLVR
no-arbitrage conditions.Comment: 21 page
Optimal investment with intermediate consumption under no unbounded profit with bounded risk
We consider the problem of optimal investment with intermediate consumption
in a general semimartingale model of an incomplete market, with preferences
being represented by a utility stochastic field. We show that the key
conclusions of the utility maximization theory hold under the assumptions of no
unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal
and dual value functions.Comment: 10 pages, revised version, to appear in the Applied Probability
Journal
Simplified mean-variance portfolio optimisation
We propose a simplified approach to mean-variance portfolio problems by changing their parametrisation from trading strategies to final positions. This allows us to treat, under a very mild no-arbitrage-type assumption, a whole range of quadratic optimisation problems by simple mathematical tools in a unified and model-independent way. We provide explicit formulas for optimal positions and values, connections between the solutions to the different problems, two-fund separation results, and explicit expressions for indifference value
Valuation of general GMWB annuities in a low interest rate environment
Variable annuities with Guaranteed Minimum Withdrawal Benefits (GMWB) entitle the policy holder to periodic withdrawals together with a terminal payoff linked to the performance of an equity fund. In this paper, we consider the valuation of a general class of GMWB annuities, allowing for step-up, bonus and surrender features, taking also into account mortality risk and death benefits. When dynamic withdrawals are allowed, the valuation of GMWB annuities leads to a stochastic optimal control problem, which we address here by dynamic programming techniques. Adopting a Hull-White interest rate model, correlated with the equity fund, we propose an efficient tree-based algorithm. We perform a thorough analysis of the determinants of the market value of GMWB annuities and of the optimal withdrawal strategies. In particular, we study the impact of a low/negative interest rate environment. Our findings indicate that low/negative rates profoundly affect the optimal withdrawal behaviour and, in combination with step-up and bonus features, increase significantly the fair values of GMWB annuities, which can only be compensated by large management fees
Martingale spaces and representations under absolutely continuous changes of probability
In a fully general setting, we study the relation between martingale spaces under two locally absolutely continuous probabilities and prove that the martingale represen- tation property (MRP) is always stable under locally absolutely continuous changes of probability. Our approach relies on minimal requirements, is constructive and, as shown by a simple example, enables us to study situations which cannot be covered by the existing theory
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