Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability-for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability—for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences. We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and Žitković (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk λ^ and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with λ^ and with the leverage being proportional to the investor’s confidence in her estimate

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences. We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and Žitković (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk λ^ and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with λ^ and with the leverage being proportional to the investor’s confidence in her estimate

Dual attainment for the martingale transport problem

We investigate existence of dual optimizers in one-dimensional martingale optimal transport problems. While [Ann. Probab. 45 (2017) 3038–3074] established such existence for weak (quasi-sure) duality, [Finance Stoch. 17 (2013) 477–501] showed existence for the natural stronger (pointwise) duality may fail even in regular cases. We establish that (pointwise) dual maximizers exist when y↦c(x,y) is convex, or equivalent to a convex function. It follows that when marginals are compactly supported, the existence holds when the cost c(x,y) is twice continuously differentiable in y. Further, this may not be improved as we give examples with c(x,⋅)∈C2−ε, ε>0, where dual attainment fails. Finally, when measures are compactly supported, we show that dual optimizers are Lipschitz if c is Lipschitz

Dual attainment for the martingale transport problem

We investigate existence of dual optimizers in one-dimensional martingale optimal transport problems. While [Ann. Probab. 45 (2017) 3038–3074] established such existence for weak (quasi-sure) duality, [Finance Stoch. 17 (2013) 477–501] showed existence for the natural stronger (pointwise) duality may fail even in regular cases. We establish that (pointwise) dual maximizers exist when y↦c(x,y) is convex, or equivalent to a convex function. It follows that when marginals are compactly supported, the existence holds when the cost c(x,y) is twice continuously differentiable in y. Further, this may not be improved as we give examples with c(x,⋅)∈C2−ε, ε>0, where dual attainment fails. Finally, when measures are compactly supported, we show that dual optimizers are Lipschitz if c is Lipschitz