Reflected backward stochastic differential equations and a class of non-linear dynamic pricing rule

@article{Morlais2008ReflectedBS,
  title={Reflected backward stochastic differential equations and a class of non-linear dynamic pricing rule},
  author={Marie-Am{\'e}lie Morlais},
  journal={Stochastics},
  year={2008},
  volume={85},
  pages={1 - 26}
}
  • M. Morlais
  • Published 15 February 2008
  • Mathematics
  • Stochastics
In this paper, we provide a characterization of solutions of specific reflected backward stochastic dfferential Equations, whose generator g has quadratic growth w.r.t its variable z: this is achieved by introducing an extended notion of g-Snell envelope. In the case when g is convex (w.r.t z), the solution is related to the notion of convex risk measures and, more specifically here, to the robust representation of one class of dynamic monetary concave functionals already introduced in a… 
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References

SHOWING 1-10 OF 56 REFERENCES
Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem
TLDR
A class of quadratic backward stochastic differential equations, which arises naturally in the utility maximization problem with portfolio constraints, is studied.
Filtration-consistent nonlinear expectations and related g-expectations
Abstract From a general definition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive, under rather general assumptions, the notions of conditional
Dynamic exponential utility indifference valuation
We study the dynamics of the exponential utility indifference value process C(B;\alpha) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that
Backward stochastic differential equations and partial differential equations with quadratic growth
We provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs) when the coefficient (or generator) F(t, Y, Z) is continuous and has a
Convex measures of risk and trading constraints
TLDR
The notion of a convex measure of risk is introduced, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and a corresponding extensions of the representation theorem in terms of probability measures on the underlying space of scenarios are proved.
Pricing Via Utility Maximization and Entropy
In a financial market model with constraints on the portfolios, define the price for a claim C as the smallest real number p such that supπ E[U(XTx+p, π−C)]≥ supπ E[U(XTx, π)], where U is the
Time consistent dynamic risk processes
Utility maximization in a jump market model
TLDR
To solve the financial problem of utility maximization in a financial market allowing jumps, this paper first proves existence and uniqueness results for the introduced BSDE, which allows the expression of the value function and characterize optimal strategies for the problem.
Optional decompositions under constraints
Summary. Motivated by a hedging problem in mathematical finance, El Karoui and Quenez [7] and Kramkov [14] have developed optional versions of the Doob-Meyer decomposition which hold simultaneously
Reflected solutions of backward SDE's, and related obstacle problems for PDE's
We study reflected solutions of one-dimensional backward stochastic differential equations. The “reflection” keeps the solution above a given stochastic process. We prove uniqueness and existence
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