• Corpus ID: 245986545

# Pricing principle via Tsallis relative entropy in incomplete market

@inproceedings{Tian2022PricingPV,
title={Pricing principle via Tsallis relative entropy in incomplete market},
author={Dejian Tian},
year={2022}
}
• D. Tian
• Published 14 January 2022
• Mathematics
A pricing principle is proposed for non-attainable q-exponential bounded contingent claims in an incomplete Brownian motion market setting. This pricing functional is compatible with prices for attainable claims, and it is defined by the solution of a specific quadratic backward stochastic differential equation (BSDE). Except translation invariance, the pricing principle processes lots of elegant properties, such as monotonicity, time consistency, concavity etc. Tsallis relative entropy theory…
2 Citations
PR ] 2 F eb 2 02 2 One-dimensional reflected BSDEs with quadratic growth generators
• Mathematics
• 2021
In this paper, we study the existence, uniqueness and comparison theorem for solutions of one-dimensional reflected backward stochastic differential equations (RBSDEs) with one continuous obstacle.
One-dimensional reflected BSDEs and BSDEs with quadratic growth generators
• Mathematics
• 2021
: In this paper, we study the existence, uniqueness and comparison theorems for solutions of one-dimensional reﬂected backward stochastic diﬀerential equations (RBSDEs) with one continuous obstacle

## References

SHOWING 1-10 OF 51 REFERENCES
A Generalized Stochastic Differential Utility
• Economics
Math. Oper. Res.
• 2003
A utility functional of state-contingent consumption plans that exhibits a local dependency with respect to the utility intensity process (the integrand of the quadratic variation) and is called the generalized SDU, which permits more flexibility in the separation between risk aversion and intertemporal substitution.
Convex pricing by a generalized entropy penalty
In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims.
Pricing Via Utility Maximization and Entropy
• Economics
• 2000
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
Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences
• Economics
Math. Oper. Res.
• 2016
In the special case where all agents have preferences of the same type and in equilibrium, all random endowments are replicable by trading in the financial market, it is shown that a one-fund theorem holds and an explicit expression for the equilibrium pricing kernel is given.
MINIMAL ENTROPY–HELLINGER MARTINGALE MEASURE IN INCOMPLETE MARKETS
• Mathematics
• 2005
This paper defines an optimization criterion for the set of all martingale measures for an incomplete market model when the discounted price process is bounded and quasi‐left continuous. This
Optimal Consumption and Portfolio Selection with Stochastic Differential Utility
• Economics
• 1999
This paper develops the utility gradient (or martingale) approach for computing portfolio and consumption plans that maximize stochastic differential utility (SDU), a continuous-time version of
Exponential Hedging and Entropic Penalties
• Mathematics
• 2002
We solve the problem of hedging a contingent claim B by maximizing the expected exponential utility of terminal net wealth for a locally bounded semimartingale X. We prove a duality relation between
Dynamic utility indierence valuation via convex risk measures
The (subjective) indierence value of a payo in an incomplete finan- cial market is that monetary amount which leaves an agent indierent between buying or not buying the payo when she always optimally
Dynamic exponential utility indifference valuation
• Mathematics
• 2005
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
Pricing, Hedging and Optimally Designing Derivatives via Minimization of Risk Measures
• Economics
• 2007
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult.