McMaster University Canada

Thomas Piketty's influential book “Capital in the Twenty-First Century” documents the marked and unequivocal rise of income and wealth inequality observed across the developed world 
in the last three decades. His extrapolations into the distant future are much more controversial and has 
has been subject to various criticisms from both mainstreams and heterodox economists. This motivates the search for an alternative standpoint incorporating 
heterodox insights such as endogenous money and the lessons from the Cambridge capital controversies. We argue that the Goodwin-Keen approach paves the road towards such an alternative.
We first consider a modified Goodwin-Keen model driven by consumption by households, instead of investment by firms, leading to the same qualitative features 
of the original Keen 1995 model, namely the existence of an undesirable equilibrium characterized by infinite private debt ratio and zero employment, 
in addition to a desirable one with finite debt and non-zero employment. By further subdividing the household sector into workers and investors, we are able to investigate their relative 
income and wealth ratios for in the context of these two long-run equilibria, providing a testable link between asymptotic inequality and private debt accumulation.

A stock loan is a contract between two parties: the lender, usually a bank or other financial institution providing a loan, and the borrower, represented by a client who owns one share of a stock used as collateral for the loan. Several reasons might motivate the client to get into such a deal. For example he might not want to sell his stock or even face selling restrictions, while at the same time being in need of available funds to attend to another financial operation. In Xia and Zhou (2007), a stock loan is modeled as a perpetual American option with a time varying strike and analyzed in detail within the Black-Scholes framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite we obtain an exact formula for the value of the loan fee to be charged by the bank based on a result in Henderson (2007). For loans of finite maturity, we characterize its value using a variational inequality first presented in Oberman and Zariphopoulou (2003). In both cases we show analytically how the fee varies with the model parameters and illustrate the results numerically. This is joint work with Cesar G. Velez (Universidad Nacional de Colombia).