4:30pm–5:00pm

Liquidity risk and optimal dividend/investment strategies. (Contributed talk)

Vathana Ly Vath*, ENSIIE; Etienne Chevalier, University of Evry; Mhamed Gaigi, ENIT

In this paper, we consider the problem of determining an optimal control on the dividend and investment policy of a firm operating under uncertain environment and risk constraints. In classical models in corporate finance, it is generally assumed that firm’s assets are either infinitely liquid or illiquid. It is particularly the case in the study of optimal dividend and investment policy. In Jeanblanc-Shiryaev (95), Asmussen-Taksar (97), Choulli-Taksar-Zhou (03), it is assumed that the firm’s assets may be separated into two types of assets, highly liquid assets which may be assimilated as cash reserve, i.e. cash and equivalents, or infinitely illiquid assets, i.e. productive assets that may not be sold. As such, when the cash reserve gets near the bankruptcy point, the firm manager may not be able to inject any cash by selling parts of its non-liquid assets. Some extensions of the above studies are investigated, see for instance Decamps-Villeneuve (05) and LyVath-Pham-Villeneuve (08) where investments are allowed. However, the core assumption on the two different types of assets, highly liquid and infinitely illiquid, still remains.

In our paper, we no longer simplify the optimal dividend and investment problem by assuming that firm’s assets are either infinitely illiquid or liquid. For the same reason as highlighted in financial market problems, it is necessary to take into account the liquidity constraints. More precisely, investment (acquiring productive assets) and disinvestment should be possible but not necessarily at their fair value. The firm may face some liquidity costs when buying or selling assets. While taking into account liquidity constraints and costs has become the norm in recent financial markets problems, it is still not the case in corporate finance, to the best of our knowledge. In our paper, we consider the company’s assets are separated in

two categories, cash and equivalents and risky assets which are subjected to liquidity costs. The risky assets are assimilated to productive assets which may be increased or decreased when the firm decides to invest or disinvest. The objective of the firm manager is to find the optimal dividend and investment strategy maximizing its shareholders’ value. Mathematically, we formulate this problem as a combined multidimensional singular and multi-regime switching problem. The studies that are most relevant

to our problem include Guo-Tomecek (08) , LyVath-Pham-Villeneuve(08), and Chevalier-LyVath-Scotti (13). By incorporating uncertainty into illiquid assets value, we no longer deal with a uni-dimensional control problem but a bi-dimensional singular and multi-regime switching problem. In such a setting, it is clear that it will be no longer possible to get explicit or quasi-explicit optimal strategies. Consequently, to determine the four regions comprising the continuation, dividend and investment/disinvestment regions, numerical resolutions are

required.

5:00pm–5:30pm

Financial Models with Defaultable Numéraires

Sergio Pulido Nino*, ENSIIE / Université d’Évry; Travis Fisher, ; Johannes Ruf,

Financial models are studied where each asset may potentially lose value relative to any other. To this end, the paradigm of a pre-determined numéraire is abandoned in favour of a symmetrical point of view where all assets have equal priority. This approach yields novel versions of the Fundamental Theorems of Asset Pricing, which clarify and extend non-classical pricing formulas used in the financial community. Furthermore, conditioning on non-devaluation, each asset can serve as proper numéraire and a classical no-arbitrage condition can be formulated. It is shown when and how these local conditions can be aggregated to a global no-arbitrage condition.

5:30pm–6:00pm

The Sustainable Black-Scholes Equation

Stéphane Crépey*, University of Evry; Yannick Armenti, University of Evry and LCH.Clearnet; Chao Zhou, National University of Singapore

In incomplete markets, a basic Black-Scholes perspective has to be complemented by the valuation of market imperfections. Otherwise this results in Black-Scholes Ponzi schemes, such as the ones at the core of the last global financial crisis, where always more derivatives are issued to remunerate the capital required by the already opened positions. In this paper we consider the sustainable Black-Scholes equations that arise for a portfolio of options if one adds to their trade additive Black-Scholes price, on top of a nonlinear liquidity funding cost, the cost of remunerating at a hurdle rate the residual risk left by imperfect hedging. In addition, we assess the impact of model uncertainty in this setup.