The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability mean...The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.展开更多
We consider a deterministic model of market evolution with trading constraints andapply a game-theoretic approach to the superhedging problem.We obtain sufficientconditions for the game equilibrium and prove under thes...We consider a deterministic model of market evolution with trading constraints andapply a game-theoretic approach to the superhedging problem.We obtain sufficientconditions for the game equilibrium and prove under these conditions the existenceof a Borel-measurable transition kernel describing dependence on price prehistory ofthe most unfavourable mixed strategy of the market.展开更多
The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w...The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In this paper we establish a version of the Kramkov's optional decomposition theorem in the setting of equivalent martingale measures. Based on this theorem, we have a new look at some basic concepts in arbitrage pricing theory: superhedging, fair price,attainable contingent claims, complete markets and etc.展开更多
It is well known that the minimal superhedging price of a contingent claim is too high for practical use.In a continuous-time model uncertainty framework,we consider a relaxed hedging criterion based on acceptable sho...It is well known that the minimal superhedging price of a contingent claim is too high for practical use.In a continuous-time model uncertainty framework,we consider a relaxed hedging criterion based on acceptable shortfall risks.Combining existing aggregation and convex dual representation theorems,we derive duality results for the minimal price on the set of upper semicontinuous discounted claims.展开更多
文摘The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.
基金supported by Moscow Center of Fundamental and Applied Mathematics(No.75-15-2022-284).
文摘We consider a deterministic model of market evolution with trading constraints andapply a game-theoretic approach to the superhedging problem.We obtain sufficientconditions for the game equilibrium and prove under these conditions the existenceof a Borel-measurable transition kernel describing dependence on price prehistory ofthe most unfavourable mixed strategy of the market.
基金The main results of this paper were reported in ref. [6]without giving the proofs.
文摘The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In this paper we establish a version of the Kramkov's optional decomposition theorem in the setting of equivalent martingale measures. Based on this theorem, we have a new look at some basic concepts in arbitrage pricing theory: superhedging, fair price,attainable contingent claims, complete markets and etc.
文摘It is well known that the minimal superhedging price of a contingent claim is too high for practical use.In a continuous-time model uncertainty framework,we consider a relaxed hedging criterion based on acceptable shortfall risks.Combining existing aggregation and convex dual representation theorems,we derive duality results for the minimal price on the set of upper semicontinuous discounted claims.
