We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that tra
ders relatively more exposed to market risk tend to submit more elastic demand functions. Noncompetitive equilibrium prices and allocations result as an outcome of a game among traders. General sufficient conditions for existence and uniqueness of such equilibrium are provided, with an extensive analysis of two-trader transactions. Even though strategic behaviour causes inefficient social allocations, traders with sufficiently high risk tolerance and/or large initial exposure to market risk obtain more utility gain in the noncompetitive equilibrium, when compared to the competitive one.
We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete market model among a group of agents whose preference is characterized by cash invariant time-consistent monetary utilities. An assumption of smallness
type is shown to be sufficient for existence and uniqueness. In particular, this assumption encapsulates settings with small endowments, small time-horizon, or a large population of weakly heterogeneous agents. Central role in our analysis is played by a fully-coupled nonlinear system of quadratic BSDEs.
The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents strategic sets consist of all possible sharing securities and p
ricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that agents best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to exist for arbitrary number of agents and be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different than their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium as compared to the Arrow-Debreu one.
In a general semimartingale financial model, we study the stability of the No Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with Bounded Risk) condition under initial and under progressive filtration enlargements. In both c
ases, we provide a simple and general condition which is sufficient to ensure this stability for any fixed semimartingale model. Furthermore, we give a characterisation of the NA1 stability for all semimartingale models.
The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numeraire portfolio depends on market characteristics, which include: (a
) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, we establish the stable behavior of the numeraire portfolio when each of the aforementioned market parameters is changed in an infinitesimal way.
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a n
atural market viability assumption, namely, absence of arbitrages of the first kind, we establish that discounted asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures.
