This paper studies the stochastic modeling of market drawdown events and the fair valuation of insurance contracts based on drawdowns. We model the asset drawdown process as the current relative distance from the historical maximum of the asset value. We first consider a vanilla insurance...

In this work we study drawdowns and drawups of general diffusion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is defined as the current increase over its running minimum. The drawdown and the drawup are the first...

Trailing stop is a popular stop-loss trading strategy by which the investor will sell the asset once its price experiences a pre-specified percentage drawdown. In this paper, we study the problem of timing to buy and then sell an asset subject to a trailing stop. Under a general linear diffusion...

We study an optimal multiple stopping problem driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and...

This paper studies a class of optimal multiple stopping problems driven by Levy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher...

The share of market making conducted by high-frequency trading (HFT) firms has been rising steadily. A distinguishing feature of HFTs is that they trade intraday, ending the day flat. To shed light on the economics of HFTs, and in a departure from existing market-making theories, we model an HFT...

We model the execution of large uninformed sell orders in the presence of strategic competitive market makers. We solve for the unique symmetric equilibrium of the model in closed-form. Our equilibrium findings provide a rationale for the empirically observed patterns of (i) short orders...

We model the execution of large uninformed sell orders in the presence of strategic competitive market makers. We solve for the unique symmetric equilibrium of the model in closed-form. Our equilibrium findings provide a rationale for the empirically observed patterns of (i) short orders...

The share of market making conducted by high-frequency trading (HFT) firms has been rising steadily. A distinguishing feature of HFTs is that they trade intraday, ending the day flat. To shed light on the economics of HFTs, and in a departure from existing market-making theories, we model an HFT...

We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative L'evy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying L'evy...