307 research outputs found
Optimal stopping and a non-zero-sum Dynkin game in discrete time with risk measures induced by BSDEs
We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) g-expectation. We then consider a non-zero-sum game on discrete stopping times with two agents who aim at minimizing their respective risks. The payoffs of the agents are assessed by g-expectations (with possibly different drivers for the different players). By using the results of the first part, combined with some ideas of S. Hamadène and J. Zhang, we construct a Nash equilibrium point of this game by a recursive procedure. Our results are obtained in the case of a standard Lipschitz driver g without any additional assumption on the driver besides that ensuring the monotonicity of the corresponding g-expectation
Theoretical and methodical foundations of assessment of foreign economic security of Ukraine Π’Π΅ΠΎΡΠ΅ΡΠΈΠΊΠΎ-ΠΌΠ΅ΡΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΎΡΠ½ΠΎΠ²Ρ ΠΎΡΠ΅Π½ΠΊΠΈ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π£ΠΊΡΠ°ΠΈΠ½Ρ
The article considers problems of assessment of foreign economic security of a country. It proves that when solving the task of analysis, assessment and modelling economic security of a state, the central place belongs to the problem of selection of the system of criteria, which would properly reflect the existing state of economy of states in a specific moment of time. It considers properties of such criteria. It analyses essence of criteria of assessment of foreign economic security. It develops a structural scheme of assessment of foreign economic security of the state, in accordance to which it is offered to consider foreign economic security as a set of three components: trade, financial and investment, and banking and credit ones. It offers a methodical approach to assessment of foreign economic security of the state, which is based on calculation of an integral indicator of security as an arithmetical mean of its components. The proposed approached is used for calculation and analysis of the level of integral indicator of foreign economic security of Ukraine in 2010 β 2011 and study of the dynamics of the level of private indicators of its three components. It builds an equation of linear regression dependence of the integral indicator of foreign economic security of a country on time and it is used as a basis for calculating forecast value of the indicator of foreign economic security of Ukraine for 2012.<br>Π ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΠΎΡΠ΅Π½ΠΊΠΈ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ ΡΡΡΠ°Π½Ρ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΈ Π·Π°Π΄Π°Ρ Π°Π½Π°Π»ΠΈΠ·Π°, ΠΎΡΠ΅Π½ΠΊΠΈ ΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π° ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΎΠ΅ ΠΌΠ΅ΡΡΠΎ Π·Π°Π½ΠΈΠΌΠ°Π΅Ρ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ° Π²ΡΠ±ΠΎΡΠ° ΡΠΈΡΡΠ΅ΠΌΡ ΠΊΡΠΈΡΠ΅ΡΠΈΠ΅Π², ΠΊΠΎΡΠΎΡΡΠ΅ Π±Ρ Π°Π΄Π΅ΠΊΠ²Π°ΡΠ½ΠΎ ΠΎΡΡΠ°ΠΆΠ°Π»ΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠ΅Π΅ ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΠΊΠΈ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π° Π² ΠΊΠΎΠ½ΠΊΡΠ΅ΡΠ½ΡΠΉ ΠΌΠΎΠΌΠ΅Π½Ρ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΡΠ²ΠΎΠΉΡΡΠ²Π° ΡΠ°ΠΊΠΈΡ
ΠΊΡΠΈΡΠ΅ΡΠΈΠ΅Π². ΠΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π° ΡΡΡΠ½ΠΎΡΡΡ ΠΊΡΠΈΡΠ΅ΡΠΈΠ΅Π² ΠΎΡΠ΅Π½ΠΊΠΈ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΡΡΡΡΠΊΡΡΡΠ½Π°Ρ ΡΡ
Π΅ΠΌΠ° ΠΎΡΠ΅Π½ΠΊΠΈ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π°, ΡΠΎΠ³Π»Π°ΡΠ½ΠΎ ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΡΡ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡ Π² ΡΠΎΠ²ΠΎΠΊΡΠΏΠ½ΠΎΡΡΠΈ ΡΡΠ΅Ρ
ΡΠΎΡΡΠ°Π²Π»ΡΡΡΠΈΡ
: ΡΠΎΡΠ³ΠΎΠ²ΠΎΠΉ, ΡΠΈΠ½Π°Π½ΡΠΎΠ²ΠΎ-ΠΈΠ½Π²Π΅ΡΡΠΈΡΠΈΠΎΠ½Π½ΠΎΠΉ ΠΈ Π±Π°Π½ΠΊΠΎΠ²ΡΠΊΠΎ-ΠΊΡΠ΅Π΄ΠΈΡΠ½ΠΎΠΉ. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΌΠ΅ΡΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ ΠΊ ΠΎΡΠ΅Π½ΠΊΠ΅ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π°, ΠΊΠΎΡΠΎΡΡΠΉ Π±Π°Π·ΠΈΡΡΠ΅ΡΡΡ Π½Π° ΡΠ°ΡΡΠ΅ΡΠ΅ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ ΠΊΠ°ΠΊ ΡΡΠ΅Π΄Π½Π΅Π°ΡΠΈΡΠΌΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ Π΅Π³ΠΎ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° ΡΠ°ΡΡΡΠΈΡΠ°Π½Ρ ΠΈ ΠΏΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Ρ ΡΡΠΎΠ²Π΅Π½Ρ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π£ΠΊΡΠ°ΠΈΠ½Ρ Π² 2010 β 2011 Π³ΠΎΠ΄Π°Ρ
ΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Π° Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ° ΡΡΠΎΠ²Π½Ρ ΡΠ°ΡΡΠ½ΡΡ
ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΡΡΠ΅Ρ
Π΅Π³ΠΎ ΡΠΎΡΡΠ°Π²Π»ΡΡΡΠΈΡ
. ΠΠΎΡΡΡΠΎΠ΅Π½ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠΉ ΡΠ΅Π³ΡΠ΅ΡΡΠΈΠΎΠ½Π½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ ΡΡΡΠ°Π½Ρ ΠΎΡ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΈ Π½Π° Π΅Π³ΠΎ Π±Π°Π·Π΅ ΡΠ°ΡΡΡΠΈΡΠ°Π½ΠΎ ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΠΎΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ Π²Π½Π΅ΡΠ½Π΅ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ Π±Π΅Π·ΠΎΠΏΠ°ΡΠ½ΠΎΡΡΠΈ Π£ΠΊΡΠ°ΠΈΠ½Ρ Π½Π° 2012 Π³ΠΎΠ΄
On the strict value of the non-linear optimal stopping problem
We address the non-linear strict value problem in the case of a general filtration and a completely irregular pay-off process (ΞΎt). While the value process (Vt) of the non-linear problem is only right-uppersemicontinuous, we show that the strict value process (V+t) is necessarily right-continuous. Moreover, the strict value process (V+t) coincides with the process of right-limits (Vt+) of the value process. As an auxiliary result, we obtain that a strong non-linear f-supermartingale is right-continuous if and only if it is right-continuous along stopping times in conditional f-expectation
Optimal stopping with f-expectations: The irregular case
We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the payoff process ΞΎ and in the case of a general filtration. We show that the value family can be aggregated by an optional process Y. We characterize the process Y as the Ef-Snell envelope of ΞΎ. We also establish an infinitesimal characterization of the value process Y in terms of a Reflected BSDE with ΞΎ as the obstacle. To do this, we first establish some useful properties of irregular RBSDEs, in particular an existence and uniqueness result and a comparison theorem
BSDEs with Default Jump
We study (nonlinear) Backward Stochastic Differential Equations (BSDEs) driven by a Brownian motion and a martingale attached to a default jump with intensity process Ξ»β=β(Ξ»t). The driver of the BSDEs can be of a generalized form involving a singular optional finite variation process. In particular, we provide a comparison theorem and a strict comparison theorem. In the special case of a generalized Ξ»-linear driver, we show an explicit representation of the solution, involving conditional expectation and an adjoint exponential semimartingale; for this representation, we distinguish the case where the singular component of the driver is predictable and the case where it is only optional. We apply our results to the problem of (nonlinear) pricing of European contingent claims in an imperfect market with default. We also study the case of claims generating intermediate cashflows, in particular at the default time, which are modeled by a singular optional process. We give an illustrating example when the seller of the European option is a large investor whose portfolio strategy can influence the probability of default
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