7,272 research outputs found
Regularity of the Optimal Stopping Problem for Jump Diffusions
The value function of an optimal stopping problem for jump diffusions is
known to be a generalized solution of a variational inequality. Assuming that
the diffusion component of the process is nondegenerate and a mild assumption
on the singularity of the L\'{e}vy measure, this paper shows that the value
function of this optimal stopping problem on an unbounded domain with
finite/infinite variation jumps is in with . As a consequence, the smooth-fit property holds.Comment: To Appear in the SIAM Journal on Control and Optimizatio
Asymptotic Glosten Milgrom equilibrium
This paper studies the Glosten Milgrom model whose risky asset value admits
an arbitrary discrete distribution. Contrast to existing results on insider's
models, the insider's optimal strategy in this model, if exists, is not of
feedback type. Therefore a weak formulation of equilibrium is proposed. In this
weak formulation, the inconspicuous trade theorem still holds, but the
optimality for the insider's strategy is not enforced. However, the insider can
employ some feedback strategy whose associated expected profit is close to the
optimal value, when the order size is small. Moreover this discrepancy
converges to zero when the order size diminishes. The existence of such a weak
equilibrium is established, in which the insider's strategy converges to the
Kyle optimal strategy when the order size goes to zero
Point process bridges and weak convergence of insider trading models
We construct explicitly a bridge process whose distribution, in its own
filtration, is the same as the difference of two independent Poisson processes
with the same intensity and its time 1 value satisfies a specific constraint.
This construction allows us to show the existence of Glosten-Milgrom
equilibrium and its associated optimal trading strategy for the insider. In the
equilibrium the insider employs a mixed strategy to randomly submit two types
of orders: one type trades in the same direction as noise trades while the
other cancels some of the noise trades by submitting opposite orders when noise
trades arrive. The construction also allows us to prove that Glosten-Milgrom
equilibria converge weakly to Kyle-Back equilibrium, without the additional
assumptions imposed in \textit{K. Back and S. Baruch, Econometrica, 72 (2004),
pp. 433-465}, when the common intensity of the Poisson processes tends to
infinity
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