On the Harm of Imposing Risk of Harm

What is wrong with imposing pure risks, that is, risks that don’t materialize into harm? According to a popular response, imposing pure risks is pro tanto wrong, when and because risk itself is harmful. Call this the Harm View. Defenders of this view make one of the following two claims. On the Constitutive Claim, pure risk imposition is pro tanto wrong when and because risk constitutes diminishing one’s well-being viz. preference-frustration or setting-back their legitimate interest in autonomy. On the Contingent Claim, pure risk imposition is pro tanto wrong when and because risk has harmful consequences for the risk-bearers, such as psychological distress. This paper argues that the Harm View is plausible only on the Contingent Claim, but fails on the Constitutive Claim. In discussing the latter, I argue that both the preference and autonomy account fail to show that risk itself is constitutively harmful and thereby wrong. In discussing the former, I argue that risk itself is contingently harmful and thereby wrong but only in a narrow range of cases. I conclude that while the Harm View can sometimes explain the wrong of imposing risk when (and because) risk itself is contingently harmful, it is unsuccessful as a general, exhaustive account of what makes pure imposition wrong.

Trajectory based market models with operational assumptions

Mathematical finance makes use of stochastic processes to model sources of uncertainty in market prices. Such models have helped in the assessment of many financial situations. These approaches impose the stochastic process a priori which is then fitted to data. Hence, unchecked hypotheses can creep into the formalism and observable phenomena plays little role in building the model fundamentals. We attempt to reverse the procedure in order to include presumably more realistic price movements. Operational assumptions are used to construct a trajectory set relating discrete chart properties with investors' portfolio re-balancing preferences. By identifying features of these trajectories we can construct models that capture different sources of risk and use a geometric procedure to produce replication bounds for a contingent claim. Why a future unfolding chart fails to belong to the proposed trajectory set is testable. A preliminary risk-reward analysis based on this is also developed.

Trajectory based market models with operational assumptions

Mathematical finance makes use of stochastic processes to model sources of uncertainty in market prices. Such models have helped in the assessment of many financial situations. These approaches impose the stochastic process a priori which is then fitted to data. Hence, unchecked hypotheses can creep into the formalism and observable phenomena plays little role in building the model fundamentals. We attempt to reverse the procedure in order to include presumably more realistic price movements. Operational assumptions are used to construct a trajectory set relating discrete chart properties with investors' portfolio re-balancing preferences. By identifying features of these trajectories we can construct models that capture different sources of risk and use a geometric procedure to produce replication bounds for a contingent claim. Why a future unfolding chart fails to belong to the proposed trajectory set is testable. A preliminary risk-reward analysis based on this is also developed.

Reduced-form setting under model uncertainty with non-linear affine intensities

<p style='text-indent:20px;'>In this paper we extend the reduced-form setting under model uncertainty introduced in [<xref ref-type="bibr" rid="b5">5</xref>] to include intensities following an affine process under parameter uncertainty, as defined in [<xref ref-type="bibr" rid="b15">15</xref>]. This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically. Moreover, we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of “no arbitrage of the first kind” as in [<xref ref-type="bibr" rid="b6">6</xref>]. </p>

Asymptotic synthesis of contingent claims with controlled risk in a sequence of discrete‐time markets

We examine the connection between discrete‐time models of financial markets and the celebrated Black–Scholes–Merton (BSM) continuous‐time model in which “markets are complete.” Suppose that (a) the probability law of a sequence of discrete‐time models converges to the law of the BSM model and (b) the largest possible one‐period step in the discrete‐time models converges to zero. We prove that, under these assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected‐utility‐maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete‐time economies as she can at the continuous‐time limit. Hence, in economically significant ways, many discrete‐time models with frequent trading resemble the complete‐markets model of BSM.

A guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium

For a discrete-time superreplication problem, a guaranteed deterministic formulation is considered: the problem is to ensure a cheapest coverage of the contingent claim on an option under all scenarios which are set using a priori defined compacts, depending on the price history: price increments at each moment of time must lie in the corresponding compacts. The market is considered with trading constraints and without transaction costs. The statement of the problem is game-theoretic in nature and leads directly to the Bellman - Isaacs equations. In this article, we introduce a mixed extension of the ``market'' pure strategies. Several results concerning game equilibrium are obtained.

A Guaranteed Deterministic Approach to Superhedging—The Case of Convex Payoff Functions on Options

This paper considers super-replication in a guaranteed deterministic problem setting with discrete time. The aim of hedging a contingent claim is to ensure the coverage of possible payoffs under the option contract for all admissible scenarios. These scenarios are given by means of a priori given compacts that depend on the history of prices. The increments of the price at each moment in time must lie in the corresponding compacts. The absence of transaction costs is assumed. The game–theoretic interpretation of pricing American options implies that the corresponding Bellman–Isaacs equations hold for both pure and mixed strategies. In the present paper, we study some properties of the least favorable (for the “hedger”) mixed strategies of the “market” and of their supports in the special case of convex payoff functions.

Interest rate option hedging portfolios without bank account

Purpose This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part. Design/methodology/approach Hedging and Malliavin calculus techniques recently developed under a stochastic string framework are applied. Findings A necessary and sufficient condition for the hedging portfolio to have no bank account part is found. This condition is applied to a barrier option, and an example of a contingent claim whose hedging portfolio has a bank account part different from zero is provided. Originality/value To the best of the authors’ knowledge, this is the first time that this issue has been addressed in the literature.