arXiv subjects

Michail Anthropelos

Publications and source records attributed to Michail Anthropelos.

17 recordsLinked to original sources

arXiv2026

Log-optimality with small liability stream

In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality techniques, we derive the fourth-order expansion of the primal value function with respect to the units $\epsilon$, held in the non-traded endowment. In turn, this lays the foundation for expanding the optimal wealth process, in this context, up to second order w.r.t. $\epsilon$. The key processes underpinning the aforementioned results are given in terms of Kunita-Watanabe projections, mirroring the case of lower order expansions of similar nature. Both the case of finite and infinite horizons are treated in a unified manner.

q-fin.MF↗

arXiv2024

Continuous-time Equilibrium Returns in Markets with Price Impact and Transaction Costs

We consider an Ito-financial market at which the risky assets' returns are derived endogenously through a market-clearing condition amongst heterogeneous risk-averse investors with quadratic preferences and random endowments. Investors act strategically by taking into account the impact that their orders have on the assets' drift. A frictionless market and an one with quadratic transaction costs are analysed and compared. In the former, we derive the unique Nash equilibrium at which investors' demand processes reveal different hedging needs than their true ones, resulting in a deviation of the Nash equilibrium from its competitive counterpart. Under price impact and transaction costs, we characterize the Nash equilibrium as the (unique) solution of a system of FBSDEs and derive its closed-form expression. We furthermore show that under common risk aversion and absence of noise traders, transaction costs do not change the equilibrium returns. On the contrary, when noise traders are present, the effect of transaction costs on equilibrium returns is amplified due to price impact.

q-fin.MF↗

arXiv2024

Strategic Informed Trading and the Value of Private Information

We consider a market of risky financial assets whose participants are an informed trader, a representative uninformed trader, and noisy liquidity providers. We prove the existence of a market-clearing equilibrium when the insider internalizes her power to impact prices, but the uninformed trader takes prices as given. Compared to the associated competitive economy, in equilibrium the insider strategically reveals a noisier signal, and prices are less reactive to publicly available information. Additionally, and in direct contrast to the related literature, in equilibrium the insider's indirect utility monotonically increases in the signal precision. Therefore, the insider is motivated not only to obtain, but also to refine, her signal. Lastly, we show that compared to the competitive economy, the insider's internalization of price impact is utility improving for the uninformed trader, but somewhat surprisingly may be utility decreasing for the insider herself. This utility reduction occurs provided the insider is sufficiently risk averse compared to the uninformed trader, and provided the signal is of sufficiently low quality.

q-fin.TR↗

arXiv2022

Optimal Investment and Equilibrium Pricing under Ambiguity

We consider portfolio selection under nonparametric $α$-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion. Implied demand functions are nondifferentiable, resemble observed bid-ask spreads, and are consistent with existing parametric limiting participation results under ambiguity. Ambiguity seekers exhibit a discontinuous demand function, implying an empty set of reservation prices. If agents have identical, or sufficiently similar prior beliefs, the first-best equilibrium is no trade. Simple conditions yield the existence of a Pareto-efficient second-best equilibrium, implying that heterogeneity in ambiguity preferences is sufficient for mutually beneficial transactions among all else homogeneous traders. These equilibria reconcile many observed phenomena in liquid high-information financial markets, such as liquidity dry-ups, portfolio inertia, and negative risk premia.

econ.GN↗

arXiv2020

Competition in Fund Management and Forward Relative Performance Criteria

In an Ito-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversification settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria, leading to the respective notions of forward best-response criterion and forward Nash equilibrium. The motivation to develop such criteria comes from the need to relax various crucial, but quite stringent, existing assumptions -- such as, the a priori choices of both the market model and the investment horizon, the commonality of the latter for both managers as well as the full a priori knowledge of the competitor's policies for the best-response case. We focus on locally riskless criteria and deduce the random forward equations. We solve the CRRA cases, thus also extending the related results in the classical setting. An important by-product of the work herein is the development of forward performance criteria for investment problems in Ito-diffusion markets under the presence of correlated random endowment process for both the perfectly and the incomplete market cases.

q-fin.PM↗

arXiv2020

Nash Equilibria in Optimal Reinsurance Bargaining

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents' strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents' bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.

q-fin.RM↗

arXiv2018

Optimal Investment, Demand and Arbitrage under Price Impact

This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading, and non-linear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, non-linear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.

q-fin.MF↗

arXiv2018

Effective risk aversion in thin risk-sharing markets

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 traders 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.

q-fin.MF↗

arXiv2018

Price Impact Under Heterogeneous Beliefs and Restricted Participation

We consider a financial market in which traders potentially face restrictions in trading some of the available securities. Traders are heterogeneous with respect to their beliefs and risk profiles, and the market is assumed thin: traders strategically trade against their price impacts. We prove existence and uniqueness of a corresponding equilibrium, and provide an efficient algorithm to numerically obtain the equilibrium prices and allocations given market's inputs. We find that restrictions may increase the market's welfare if traders have different views regarding the covariance matrix of securities returns. The latter heterogeneity regarding covariance matrix disagreement is essential in modelling; for instance, when traders agree on the covariance matrix, restricting participation in some securities for some traders leaves equilibrium prices unaltered in the unrestricted securities, a certainly undesirable model effect.

econ.GN↗

arXiv2016

The pricing of contingent claims and optimal positions in asymptotically complete markets

We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated Gärtner-Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, models of large markets with vanishing trading restrictions and the Black-Scholes-Merton model with either vanishing default probabilities or vanishing transaction costs. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models.

q-fin.MF↗

arXiv2016

Equilibrium in risk-sharing games

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 pricing 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.

q-fin.RM↗

arXiv2016

The Effect of Market Power on Risk-Sharing

The paper studies an oligopolistic equilibrium model of financial agents who aim to share their random endowments. The risk-sharing securities and their prices are endogenously determined as the outcome of a strategic game played among all the participating agents. In the complete-market setting, each agent's set of strategic choices consists of the security payoffs and the pricing kernel that are consistent with the optimal-sharing rules; while in the incomplete setting, agents respond via demand functions on a vector of given tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium, the sharing securities are suboptimal, since agents submit for sharing different risk exposures than their true endowments. On the other hand, the Nash equilibrium prices stay unaffected by the game only in the special case of agents with the same risk aversion. In addition, agents with sufficiently lower risk aversion act as predatory traders, since they absorb utility surplus from the high risk averse agents and reduce the efficiency of sharing. The main results of the paper also hold under the generalized models that allow the presence of noise traders and heterogeneity in agents' beliefs.

q-fin.GN↗

arXiv2015

An equilibrium model for spot and forward prices of commodities

We consider a market model that consists of financial investors and producers of a commodity. Producers optionally store some production for future sale and go short on forward contracts to hedge the uncertainty of the future commodity price. Financial investors take positions in these contracts in order to diversify their portfolios. The spot and forward equilibrium commodity prices are endogenously derived as the outcome of the interaction between producers and investors. Assuming that both are utility maximizers, we first prove the existence of an equilibrium in an abstract setting. Then, in a framework where the consumers' demand and the exogenously priced financial market are correlated, we provide semi-explicit expressions for the equilibrium prices and analyze their dependence on the model parameters. The model can explain why increased investors' participation in forward commodity markets and higher correlation between the commodity and the stock market could result in higher spot prices and lower forward premia.

econ.GN↗

arXiv2013

Forward Exponential Performances: Pricing and Optimal Risk Sharing

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the comparison between the forward exponential and the backward exponential utility indifference valuation. In addition, we construct the problem of optimal risk sharing in this forward setting and solve it when the agents' forward performance criteria are exponential.

q-fin.PM↗

arXiv2012

On contingent claims pricing in incomplete markets: A risk sharing approach

In an incomplete market setting, we consider two financial agents, who wish to price and trade a non-replicable contingent claim. Assuming that the agents are utility maximizers, we propose a transaction price which is a result of the minimization of a convex combination of their utility differences. We call this price the risk sharing price, we prove its existence for a large family of utility functions and we state some of its properties. As an example, we analyze extensively the case where both agents report exponential utility.

q-fin.CP↗

arXiv2009

Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability

In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents' risk preferences are modelled by convex capital requirements, we define and analyze their demand functions and propose a notion of a partial equilibrium price. In addition to sufficient conditions for the existence and uniqueness, we also show that the equilibrium prices are stable with respect to misspecifications of agents' risk preferences.

q-fin.RM↗

arXiv2008

On Agents' Agreement and Partial-Equilibrium Pricing in Incomplete Markets

We consider two risk-averse financial agents who negotiate the price of an illiquid indivisible contingent claim in an incomplete semimartingale market environment. Under the assumption that the agents are exponential utility maximizers with non-traded random endowments, we provide necessary and sufficient conditions for negotiation to be successful, i.e., for the trade to occur. We also study the asymptotic case where the size of the claim is small compared to the random endowments and we give a full characterization in this case. Finally, we study a partial-equilibrium problem for a bundle of divisible claims and establish existence and uniqueness. A number of technical results on conditional indifference prices are provided.

q-fin.PR↗