Albina Danilova

Stock market insider trading in continuous time with imperfect dynamic information

In this paper, I study the equilibrium pricing of asset shares in the presence of dynamic private information. The market consists of a risk-neutral informed agent who observes the firm value, noise traders and competitive market makers who set share prices using the total order flow as a noisy signal of the insiders information. I provide a characterization of all optimal strategies and prove the existence of both Markovian and non-Markovian equilibria by deriving closed-form solutions for the optimal order process of the informed trader and the optimal pricing rule of the market maker. The consideration of non-Markovian equilibrium is relevant since the market maker might decide to re-weight past information after receiving a new signal. Also, I show that (1) there is a unique Markovian equilibrium price process that allows the insider to trade undetected and (2) the presence of an insider increases the markets informational efficiency, in particular, for times close to dividend payment.

Equilibrium model with default and dynamic insider information

We consider an equilibrium model à la Kyle–Back for a defaultable claim issued by a given firm. In such a market the insider observes continuously in time the value of the firm, which is unobservable by the market makers. Using the construction in Campi et al. (http://hal.archives-ouvertes.fr/hal-00534273/en/, 2011) of a dynamic three-dimensional Bessel bridge, we provide the equilibrium price and the insider’s optimal strategy. As in Campi and Çetin (Finance Stoch. 11:591–602, 2007), the information released by the insider while trading optimally makes the default time predictable in the market’s view at the equilibrium. We conclude the paper by comparing the insider’s expected profits in the static and dynamic private information case. We also compute explicitly the value of the insider’s information in the special cases of a defaultable stock and a bond.

Financial Markets with Informational Asymmetries and Equilibrium

This chapter introduces the setup for the equilibrium models that extends, among others, the works of Kyle and Back. It also contains some key results that will be relevant for the characterisation of the equilibrium. Finally the equilibrium will be derived and discussed in Chaps. 7 and 8.

Kyle—Back Model with Default and Dynamic Information

In this chapter we will continue applying the dynamic bridge construction from Chap. 5 to solve the Kyle–Back model in the case of dynamic information and default risk.

Stochastic Differential Equations and Martingale Problems

In this chapter we explore the well posedness of martingale problems of Stroock and Varadhan. The results of this chapter will be crucial for solving the filtering equations of Chap. 3. This well posedness will be obtained by establishing the relationship between solutions of martingale problems and stochastic differential equations (SDEs). Thus, our focus in this chapter will be the connection between SDEs and martingale problems. To formulate the martingale problem we first need to develop the notion of an infinitesimal generator.

Static Markov Bridges and Enlargement of Filtrations

In the applications considered in the second part of this book, the rational agents in equilibrium trade so as to drive the demand for the traded to a certain level at a future date.