# Poster session and reception

Tuesday, June 12, 2018 - 4:30pm - 6:00pm

Lind 400

**Sensitivity Analysis of the Financial Network Model**

Weijie Pang (Worcester Polytechnic Institute)

The financial system is increasingly interconnected. Cyclical interdependencies among corporations may cause that the default of one firm seriously affects other firms and even the whole financial network. To describe financial networks, L. Eisenberg and T. Noe introduced network models that became popular among researchers and practitioners. To describe the connections between firms, they use the liabilities between two firms to construct relative liability matrices. Based on this description, they compute the payouts of firms to their counterparties. However, in practice, there is no accurate record of the liabilities and researchers have to resort to estimation processes. Thus it is very important to understand possible errors of payouts due to the estimation errors. In our research, we quantify the clearing vector's sensitivity to such estimation errors and show that its directional derivatives are, like the clearing vector itself, solutions of fixed point equations. We describe estimation errors utilizing a basis for the space of matrices representing permissible perturbations and derive analytical solutions to the maximal deviations of the Eisenberg-Noe clearing vector. Moreover, we quantify the probability of observing clearing vector deviations of a certain magnitude, for uniformly or normally distributed errors in the relative liability matrix.**Relative forward indifference valuation of real-time incoming projects**

Haoran Wang (The University of Texas at Austin)

Classical indifference valuation approach in incomplete market is rooted in stochastic control paradigm where a backward reasoning for pricing is typically applied. Implicit assumptions are hence made such that the market model (or a family of models) is initially pre-specified, and, furthermore, the characteristics of the stream of incoming projects are known a priori. Such model commitment and projects commitment exclude the possibility of incorporating real-time model adaptation, and real-time arrival and expiration of risky projects. In this work, we present an alternative approach, based on the forward performance process, for relative valuation of asynchronously arriving projects in real-time with non-anticipated characteristics. The relative price of the incoming project depends on the solution to an ill-posed HJB equation that also yields the underlying exponential forward process. We further discuss the additivity property of prices, residual optimal wealth processes and residual risk processes, associated with both the existing project and the incoming project. Joint with T. Zariphopoulou**Optimal dividend strategies with Levy-type accumulated interest rate**

Huanqun Jiang (Oregon State University)

De Finetti's dividend distribution problem has been studied for a long time. The optimality of dividend strategies has been proved in various cases including linear diffusion, Compound Poisson, dual model, spectrally negative(positive) Levy process, etc. We will introduce the eigenfunction of extended generator of Levy process. Then we will see that the optimality of dividend strategies can be proved under the circumstance that the accumulated interest rate behaves with Levy noise. The proof relies on the property and fluctuation idendities from scale function of spectrally negative Levy process.**Convexity of ruin probabilities in insurance risk models**

Sooie-Hoe Loke (Central Washington University)

Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization problem is given. This is a joint work with David Landriault, Bin Li, Gordon Willmot, and Di Xu.**The Optimal Execution Strategy of Employee Stock Option**

Yi Fu (North Carolina State University)

In this paper, we develop an optimal execution strategy for employee stock options by means of the fluid model, in which a voluntary turnover is considered. We show that the value function is the viscosity solution of the Hamilton-Jacobi-Bellman variational inequality and prove the uniqueness of the viscosity solution. Finally, we present numerical illustrative examples and numerical solutions of optimal strategies which are computed by the finite difference method.**Valuation of Equity-linked Insurance Products**

Hailiang Yang (University of Hong Kong)

Nowadays, many insurance companies and financial institutions are involved in trading variable annuity and equity-indexed insurance contracts. The contractual structures of these products are more sophisticated than traditional insurance products. In particular, these products contain various exotic derivatives features. Therefore, advanced quantitative tools and methods are required for the valuation of these products. This leads to a practically relevant and challenging research problem. In this work, a substantial series of closed-form formulas is obtained for various contingent options. This is a joint work with Hans Gerber and Elias Shiu.**Explicit Solutions for Optimal Resource Extraction Problems under Regime Switching Levy Models**

Moustapha Pemy (Towson State University)

This paper studies the problem of optimally extracting nonrenewable natural resources. Taking into account the fact that the market values of natural resources fluctuate randomly following various global and seasonal macroeconomic factors, the prices of natural resources are modeled using Markov switching Levy processes. We formulate this problem as finite-time horizon optimal control problem. We derive closed-form solutions for the value function as well as the optimal extraction policy. Numerical examples are presented to illustrate these results.